The Reds took the lead inside eight minutes when Jordan Henderson met Trent Alexander-Arnold's corner with a thunderous header, but Wolves deservedly levelled six minutes after the break when Raul Jimenez nodded in Adama Traore's cross.
Both teams passed up good chances as the game seemed to be heading for a stalemate till Firmino’s moment of magic secured a 14th straight win for the league leaders.
The Merseyside-based club have now extended their unbeaten Premier League run to 40 games.
Speaking after the game, Klopp singled out the performance of the former Hoffenheim man for a praise.
"We changed the system two or three times, we calmed it down,” the German coach told BBC Sports.
“We had incredible chances in the first half and then at the end it was a magic moment from Bobby [Firmino].”
"You just have to find a way to win and have someone who makes the perfect decision and that was Bobby again.”
He added: "The boys are human. It was a little bit up and down. We had discussion on the pitch, there was stuff to improve but set-pieces can bring us back in the game, a good bit of skill can bring us back in the game.”
“Wolves were really strong but it’s clear we could settle again.”
