Heslip attended Nelson High School in Burlington, Ontario where he was a three-time Halton all-star honoree and team captain in 2008–09. As a senior, he averaged 28 points, four rebounds and four assists per game. In February 2009, he scored a school-record 54 points in Nelson's game against Notre Dame. He also earned MVP honors at the 2009 All-Canada Classic.

During the 2009 Fall semester, Heslip attended New Hampton School in New Hampton, New Hampshire where he averaged 15 points and seven rebounds before enrolling at Boston College.

Heslip went mostly unrecruited, receiving an offer to play from only the University of Guelph in Ontario. However, he raised his stock after a solid summer playing in the Amateur Athletic Union (AAU). In December 2009, he joined the Boston College Eagles men's basketball team where he participated in practice but did not play for them in 2009–10. In April 2010, Heslip announced his decision to transfer from Boston College.

On June 9, 2010, Heslip signed a National Letter of Intent to play for Baylor University, and subsequently sat out the 2010–11 season due to NCAA transfer regulations. During 2010–11, he was named to the Big 12 Commissioner's Honor Roll for both the fall 2010 and spring 2011 semesters.

As a redshirted sophomore in 2011–12, Heslip was named to the Big 12 All-Tournament team, Academic All-Big 12 second team, Las Vegas Classic All-Tournament team and Big 12 Commissioner's Honor Roll for both the fall 2011 and spring 2012 semesters. In 38 games (37 starts), he averaged 10.2 points, 1.3 rebounds and 1.0 assists in 27.1 minutes per game.

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