Durrant started his career at Rangers and made his debut against Greenock Morton in April 1985. The following season, he was a regular fixture in the Rangers team and scored in his Old Firm debut that season. Durrant was fined £1500 by Rangers in 1987 after his involvement in an incident in a kebab shop after Rangers had won the league championship. In October 1988 Durrant suffered a career-threatening knee injury in a match with Aberdeen at Pittodrie. A challenge by Aberdeen's Neil Simpson left him out of competitive football for almost three years. He made his return in April 1991 in a reserve fixture against Hibernian and was welcomed back by 47,453 Rangers fans. Durrant went on to play a part in both Rangers 1992/93 Champions League and Rangers' run of finally equalling Celtic's nine successive league championships, the last of which was clinched in 1997.
In 2005 he returned to Rangers as coach of the under-19s and, later, the reserve team. Following the resignation of Paul Le Guen as Rangers manager on 4 January 2007, Durrant was temporarily elevated to the manager position at Rangers until Walter Smith was re-appointed. He lost his only game in charge of the first team, which was a Scottish Cup tie, 3-2 at the hands of Dunfermline Athletic. Durrant worked as a coach of the Rangers first team under Walter Smith and Ally McCoist. He was demoted in December 2014 to a position with the Rangers under-20 team, after McCoist left the club.