Dakich attended Andrean High School in Merrillville, Indiana. He elected to play basketball for Indiana under coach Bob Knight from 1981 to 1985. He was a team captain during his junior and senior seasons and the Hoosiers finished with an 84–39 (.683) record during his career. As a player, he helped Indiana win one Big Ten title (during the 1982–83 season), earn three NCAA Tournament berths and finish as the NIT runner-up his senior season. As a junior, he was named All-Tournament at the Indiana Classic and as a senior he earned similar accolades at the Hoosier Classic.
Dakich is remembered for his defensive effort against Michael Jordan in Indiana's upset of No. 1 ranked North Carolina in the 1984 East Regional Semifinal of the NCAA Tournament. It was Dakich's sixth start of the year, but Knight assigned him to guard Jordan the afternoon of the game. Knight told him, "Just don't let him dunk on you. That will embarrass you and me both." Dakich later reported, "I went back to my room and threw up." Jordan scored 13 points in what would be his final college game, and both Dakich and Jordan eventually fouled out of the game. Indiana won the game 72–68.
Dakich was first a graduate assistant coach at Indiana under Bob Knight from 1985–87 and then an assistant coach at Indiana from 1987 to 1997. He helped the Indiana program win 74% (283–101) of its games over the 12 years he served as an assistant coach. The Hoosiers won a national title in the 1986–87 season and earned a spot in the NCAA Tournament in each of his 12 seasons on the staff. IU also captured four Big Ten titles while finishing third or better in 9 of his 12 years.
Dakich was the academic monitor on the Indiana basketball staff his last seven years and, under his guidance, every four-year player on the program graduated. He also assisted in the development of six All-Americans and three national Player of the Year candidates, including 1993 Player of the Year Calbert Cheaney.
From 1997 to 2007 he served as the head coach at Bowling Green State University where he compiled a record of 156–140 (.527). He tied for third all-time in victories among the school's coaches and also was just one of three coaches in school history to post four 18-plus win seasons or more in men's basketball. He saw 22 of 25 seniors complete their degree requirements and had 12 former players sign professional contracts, including former Indiana Pacers guard Keith McLeod. In addition, he had two players earn MAC Player of the Year and three lead the league in scoring during his tenure. During Dakich's tenure, BGSU appeared in the NIT twice but never made it to the NCAA Tournament.
Briefly in 2002, Dakich was named head basketball coach at West Virginia University (WVU) to succeed Gale Catlett. During conversations with WVU players, Dakich learned that people affiliated with the basketball program may have been guilty of NCAA recruiting rules infractions. He allegedly attempted to renegotiate a higher salary at WVU and failed, thus returning to Bowling Green as head basketball coach after only a week at WVU. WVU voluntarily reported results of its internal investigation to the NCAA, and the university was not penalized as a result of the infractions. The focus of the investigation, Jonathan Hargett, was banned from WVU athletics for his role in the reported violations.
At the end of the 2008 season he served as the interim head coach at Indiana University, following Kelvin Sampson's resignation due to NCAA recruiting violations. Under Dakich's guidance, the Hoosiers went 0-2 in postseason play, losing in the first rounds of the Big 10 and NCAA tournaments. After the season, IU declined to offer Dakich the job on a permanent basis, opting instead for Tom Crean.
Dakich is the host of "The Dan Dakich Show" on Indianapolis radio station WFNI, ESPN radio affiliate, 1070 The Fan. Dakich served as a college basketball studio analyst for the Big Ten Network for the 2009–2010 college basketball season. Beginning in November 2010, Dakich joined ESPN as a college basketball color commentator and studio analyst, replacing Steve Lavin.