The game pitted Gerrard against his former manager at Liverpool, Brendan Rodgers, but a first Scottish Premiership win for his side over their bitter rivals since 2012 rarely looked likely in a game the Bhoys dominated.
After striking the crossbar three times, the hosts finally got the breakthrough they deserved after 62 minutes as a flowing counter-attack saw James Forrest send a cool pass across goal for Olivier Ntcham to deliver the decisive blow.
Rangers should have been reduced to 10 men in the 25th minute, but the officials failed to spot Allan McGregor's petulant kick at Kristoffer Ajer off the ball.
Moments later, Celtic hit the crossbar twice in the space of a manic minute. First, Forrest saw a deflected half-volley from 30 yards clip the top of the woodwork and from the resulting corner Mikael Lustig headed against the frame of the goal from close range.
McGregor then took full advantage of his reprieve to paw away Odsonne Edouard's back-post header as the visitors withstood intense pressure to somehow go into the break level.
Celtic picked up where they left off after the interval as they hit the crossbar for a third time, Ntcham's low drive from distance diverted onto the woodwork by McGregor's strong hand.
McGregor stood no chance with the Frenchman's goal, while Leigh Griffiths clipped the outside of the post late on as Celtic move within three points of early league leaders Hearts.