After playing with the Airdrie Extreme in 1997–98, Aulin joined the Kamloops Blazers of the Western Hockey League as 16-year-old in 1998–99, netting 26 points in 55 games and a trip to the league finals. A 55-point 1999–2000 season (57 games) attracted the attention of the Colorado Avalanche, who drafted Aulin in the second round (47th overall) of the 2000 NHL Entry Draft. In the 2000–01 season with the Blazers, Aulin scored a team leading 108 points in 70 games. During this time Aulin's rights were traded by the Avalanche to the Los Angeles Kings in an exchange that saw Rob Blake head to Colorado on March 22, 2001.
Before the end of his junior career, Aulin won silver with Team Canada at the 2002 World Junior Ice Hockey Championships, collecting 9 points in 7 tournament games.
On June 1, 2002, Aulin signed a three-year entry level contract with the Kings. Aulin made his professional debut in the following 2002–03 season with Kings affiliate, the Manchester Monarchs. During the season, Aulin also made his NHL debut with the Kings, appearing in 17 games. Aulin scored his only two goals against the Carolina Hurricanes in an 8-2 victory on February 7, 2003.
In the 2003–04 pre-season with the Kings, Aulin suffered a shoulder injury which required surgery. Aulin remained injured for the majority of the season and was subsequently traded to the Washington Capitals for Anson Carter on March 9, 2004. Jared made his return from injury with the Capitals' AHL affiliate Portland Pirates to end the season.
Aulin spent the next two seasons with the Capitals' affiliates without a call-up to the NHL. After not being offered a contract with the Capitals for the 2006–07 season, Aulin signed with the AHL Springfield Falcons on October 7, 2006. Jared played in only 13 games with the Falcons before he was released after aggravating his recurring shoulder injury.
During the summer of 2007, Aulin returned to hockey playing in a non-contact summer league with the TH Pirates in Calgary. While leading the league in scoring, Aulin was knocked unconscious and hospitalised when he was the victim of a two-handed slash to the neck in a game. Aulin pressed charges against the offender, but the incident left him jaded and considering retirement. Aulin later returned to Hockey in the 2007–08 season with the University of Calgary in the CIS. This marked the first time in 20 years that a NHL player returned to play in the CIS.
After further shoulder rehab, Aulin attempted a return to professional hockey and was invited to the Columbus Blue Jackets training camp for the 2009–10 season. He was later reassigned to the Blue Jackets' AHL affiliate, the Syracuse Crunch, training camp and made the Crunch's opening night on a try-out basis. After 31 games with Syracuse, and placing third in scoring, Aulin was signed to an AHL contract for the remainder of the season with the Crunch on January 2, 2010.
A free agent prior to the 2010–11 season, Aulin accepted a tryout invitation to the Edmonton Oilers training before he was released during the pre-season on September 27, 2010. On October 29, 2010, Aulin belatedly left North America and signed a one-year contract with Swedish team, Leksands IF, of the second tier HockeyAllsvenkan.
On June 28, 2011, Aulin signed a one-year deal to remain in the HockeyAllsvenskan with Örebro HK.
After four seasons with Örebro HK, the last two solidifying the club's position in the Swedish Hockey League, Aulin left Sweden as a free agent and signed a one-year deal with newly relegated Swiss club, Rapperswil-Jona Lakers of the NLB on June 23, 2015.