The energetic pace of the game has continued, and Rangers restored their lead midway through the second half, Daniel Candeias drilling the ball low past Bain after more uncertainty in the Celtic penalty area.
Rangers manager Graeme Murty conceded he had endured the biggest disappointment of his career by squandering "a real good opportunity to apply some pressure" to Celtic.
But Rodgers was thrilled by his team's reaction to the red card, Edouard's 69th-minute strike, coupled with staunch defence, securing the three points.
"I'm immensely frustrated for the fans and the players because we put ourselves in a right good situation". They did a lot of talking beforehand - we stayed quiet.
Murty told the media: "We have to respect what Celtic are about, we understand the threats that they bring, they didn't win the league past year for no reason". Nor has Murty, a man some of us believe should never have been handed the Ibrox job in the first place, been doing much wrong recently.
We always believed we could come here and get the three points and we did that. His manager will give him until the last minute to recover, but with Bruno Alves, who started in the 4-1 win over Falkirk last weekend, and David Bates both available they look set to start.
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"But then the players showed their qualities". I think when you come to one of your rivals, and be up against it with ten men for 30 minutes of the game left, then you are entitled to celebrate.
Simunovic's dismissal in the 57th minute appeared to give Rangers the advantage, yet it was the visitors who scored the all-important fifth goal thanks to an inspired change.
It was a day to savour for Celtic goalkeeper Scott Bain, the on-loan Dundee stopper making his debut for the club in his first senior appearance since 28 October.
"I'm desperate to experience the atmosphere", he said. "It's not a matter of whether you're playing well or not".
"People will say I should get it, people will say I shouldn't get it, people will say I will be defined by this one game", he said. For me it's a must win game for Rangers as a Celtic win ends any doubt about where the league title is going to go.