Although Parish had a successful college career at Centenary College of Louisiana from 1972–1976, he received virtually no notice because of one of the most severe penalties ever levied by the National Collegiate Athletic Association.
In 1965, the NCAA adopted the so-called "1.6 rule" to determine academic eligibility of incoming freshmen. Under its provisions, freshmen academically qualified if their high school grades and standardized test scores predicted a minimum college grade point average of 1.6 on a 4-point scale.
Parish, who led Woodlawn High School in Shreveport to the Louisiana High School Athletic Association Class AAAA state championship in 1972, took a standardized test that did not fit the NCAA's formula; Centenary converted his score to an equivalent that fit the formula, which it had done for 12 other athletes in the previous two years. This was a violation of NCAA regulations; however, the NCAA had not paid any attention to the school's actions before Parish's recruitment. Shortly before Parish was to enroll, the NCAA notified Centenary that he and four other basketball players whose test scores had been converted were ineligible to play there, but said that the school would not be subject to penalty if it rescinded the five scholarships. Centenary argued that the rule did not say that the school could not convert the scores of Parish and the other players, while the NCAA argued that Centenary could not use the test taken by Parish and the other players to establish eligibility. When Centenary refused to pull the scholarships, the NCAA issued one of the most draconian sanctions in its history. The school's basketball program was put on probation for six years, during which time it was not only barred from postseason play, but its results and statistics were excluded from weekly statistics and its existence was not acknowledged in the NCAA's annual press guides.
Within days of its decision, the NCAA repealed the 1.6 rule—but refused to make the five players eligible. A few months later, all five, including Parish, sued the NCAA for their eligibility at Centenary, but lost. The decision made Parish a sort of "invisible man" who racked up huge statistical totals in virtual obscurity. In his four years at Centenary, the Gents went 87-21 and spent 14 weeks in the AP Top 20 poll, mostly during his senior season in 1975–76. He averaged 21.6 points and 16.9 rebounds per game during his Centenary career. However, although the school recognizes his records, the NCAA to this day does not include Parish in its record books. For example, the NCAA's official Division I basketball records book includes a list of all players since the 1972–73 season (Parish's freshman year) to have averaged 15 rebounds during a season. To this day, Parish does not appear on this list, even though he averaged at least that many rebounds in each of his four seasons, and his career rebounding average is higher than that of any player on the NCAA's official list of post-1972 career rebounding leaders. The only mention of Parish's time at Centenary in the official NCAA record books is that of the Gents' appearances in the AP Poll from the 1973–74 through 1975–76 seasons.
While the Gents were on probation, another Louisiana school, the University of Southwestern Louisiana, was given the so-called "death penalty" by the NCAA in 1973 for falsifying transcripts; the Ragin' Cajuns basketball team was forbidden from playing during the 1973–74 and 1974–75 seasons. The NCAA wanted to expel Southwestern Louisiana from the NCAA, but instead stripped the school of its voting privileges at the annual convention until 1977.
Between his junior and senior years, he played for the US national team at the 1975 Pan American Games. His difficulties with the NCAA indirectly led to his not being recommended for a spot on the team. Centenary paid his way to Salt Lake City to try out; he made the team, was unanimously elected captain, and led the team to a gold medal.
Throughout his time at Centenary, Parish chose not to escape anonymity by either jumping to the National Basketball Association or American Basketball Association (the latter of which existed until the ABA–NBA merger in 1976), or by transferring to another college, even though the professional ranks offered him potential riches and a transfer would have given him eligibility and far more publicity. At the time, professional scouts did not question his physical skills, but were divided as to whether his decision to stay at Centenary was a show of loyalty or evidence of poor decision-making. One NBA scout said during Parish's senior season, "The jury is still out as to whether Parish can win games for a pro team. He can definitely play in the pros and he's going to get a lot of money, but that doesn't mean he's going to be another Abdul-Jabbar (whom he ended up passing in games played in his next-to-last season)." For his part, Parish said during the same season, "I didn't transfer because Centenary did nothing wrong. And I have no regrets. None."
After college, Parish was drafted in the first round of the 1976 NBA draft by the Golden State Warriors. He had also been drafted by the Utah Stars in the 1973 ABA Special Circumstances draft and by the Spurs in the 1975 ABA draft. Parish signed with the Warriors. The Warriors were NBA champions in 1975 (two seasons prior to Parish's rookie campaign). However, when Parish joined the Warriors, their decline had begun, and they missed the playoffs completely from 1978 to 1980.
Heading into the 1980 NBA draft, the Boston Celtics (who already had small forward Larry Bird ready to start his second NBA season) held the number one overall pick. In a pre-draft trade, Celtics President Red Auerbach dealt the top pick and an additional first-round pick to the Warriors for Parish and the Warriors' first-round pick, the third overall. With that pick, the Celtics chose Kevin McHale. The Warriors then selected Joe Barry Carroll with the first pick, whose career eventually was shortened by injuries, and whose perceived laziness earned him the moniker "Joe Barely Cares."
The Celtics now had an imposing frontcourt consisting of Bird, Parish, Cedric Maxwell, and McHale. Parish compared his transition from Golden State to Boston in a televised quote where he jokingly said it was like going from an outhouse to a penthouse. Playing 14 years with the Celtics from 1980 to 1994, Parish won three NBA titles (1981, 1984 and 1986) teaming with Bird and power forward McHale. Parish, Bird and McHale came to be known as "The Big Three." All three were named by the NBA to the NBA's 50th Anniversary All-Time Team and are regarded as one of the greatest frontcourts in NBA history.
After leaving the Celtics, Parish played two seasons with the Charlotte Hornets.
Parish played his final season with the Chicago Bulls in 1996–97, which led to his fourth NBA title. At 43, he is the third-oldest player to ever play an NBA game, behind Nat Hickey of the Providence Steamrollers and Kevin Willis of the Dallas Mavericks, and as of 2017, his 1,611 games played over 21 seasons in the NBA remain unmatched. As of 2017, he also remains the oldest player to win an NBA championship.
He was known as a versatile center, using his 7' size and speed to contain opposing players, launch precise shots from outside the paint, and finish fast breaks – the latter uncanny for a man of his stature. Fellow Hall of Famer and teammate from 1985 to 1987 Bill Walton once called Parish the "greatest shooting big man of all time", perhaps because of Parish's field goal and free throw shooting ability, an unusual talent among most centers. His trademark was his high-release jump shot, which traversed a very high arc before falling.
In 1996, Parish, along with teammates Larry Bird and Kevin McHale, were each selected as one of the 50 Greatest Players in NBA History. In 1998, in honor of his achievements, the Celtics retired Parish's famous #00 jersey number at halftime of a Celtics-Pacers game; this allowed Larry Bird, then head coach of the Pacers, to participate in the ceremony. He was enshrined in the Basketball Hall of Fame in 2003.
Parish remains active as the Celtics' team consultant and mentor for current Celtics big men.