Defeat condemns Rangers to their worst start to a league season in 29 years, with just one win - and five points - from four matches.
For Rangers, though, it was the first defeat under Gerrard and one which left their manager very unhappy.
Collum was having a busy time, booking Edouard for foul on Ryan Jack before the French forward missed a great chance from Callum McGregor's cross, heading straight at Allan McGregor who clawed the ball away for another corner which proved fruitless.
Celtic were the better team over the course of the 90 minutes, and Brendan Rodgers's side could have scored more goals against Rangers. Gerrard, however, said post-match that he heard the fourth official tell the referee it was a 'foul'.
Amid the frenzied atmosphere it was a moment of real quality midway through the second half that finally gave Celtic a deserved lead.
"The first half, we didn't make enough passes even though our shape was OK but I feel we've been done by a refereeing decision". It's blatant. For me it's 100 per cent a foul.
Rodgers admitted his side dominated the clash from start to finish but praised Steven Gerrard for the way he set Rangers up during the tie.
The former Liverpool and England captain, who played under Hoops manager Brendan Rodgers at Anfield, had yet to lose in 12 games since taking over at Ibrox before the trip to Parkhead. Steven [Gerrard] has done well getting them organised so we had to be patience.
Celtic hit the frame of the goal on four occasions, leading Rodgers to describe his side as dominant despite the tight scoreline.
"I felt we were hanging on a bit [in the first half] but I thought second half we matched them, if not edged it", he said.
Celtic have revealed their starting eleven and substitutes to play host to rivals Rangers in a Scottish Premiership encounter this afternoon.
Gerrard has made 12 new signings already this summer but is seeking further deals before the transfer deadline slams shut on Friday and we have identified three reported targets who could provide his side with a huge boost.
"There's a lot more to come from this squad".