Alex McLeish said "some titanic performances" had ended his wait for a victory at Celtic Park since taking over as Rangers manager.
"It's been a long time and it's been hanging over us, but overall I thought we deserved it," he said after a 2-0 win for the league leaders.
"We could have passed it better in the first half but improved our composure.
"It was more important for us to win than Celtic and there is a long way to go in the championship."
Celtic can draw level again should they win their game in hand.
"But it means we are now leaders in our own right and not playing catch up and we have laid that monkey," enthused McLeish.
Recent signing Ronald Waterreus had several excellent saves to prevent Celtic taking the lead and then equalise.
"He has so much experience and it was imperative that we brought in a quality goalkeeper when Stefan Klos got injured," said McLeish.
But the Rangers manager picked out right-back Alan Hutton and fellow defenders Marvin Andrews and Sotiris Kyrgiakos.
"Alan had a sticky spell, but he has been excellent since coming back in and I thought Michael Ball had his best game in a Rangers jersey," added McLeish.