The fringe striker came off the bench to strike with seconds remaining to ensure the Reds did not rue a host of missed chances at Molineux.
Chelsea's defeat to West Ham earlier on Saturday handed Jurgen Klopp's men the chance to move ahead of the European champions.
Origi's low finish from Mohamed Salah's cut-back moves Liverpool a point clear of the Blues and two ahead of Manchester City, who face Watford later on Saturday.
Liverpool had scored four goals in each of their last three league games and two or more in 18 straight games but saw that run come to an end due to a rare off day with their finishing.
Trent Alexander-Arnold volleyed over before Diogo Jota headed over the first of his big chances to score against his former club.
Salah was denied a simple tap in for his 20th goal in as many games by a miraculous last-ditch challenge from Romain Saiss to divert Andy Robertson's cross to safety.
The chances continued to come and go for Liverpool after the break, but none were bigger than the one presented to Jota midway through the half.
A mix up between Wolves goalkeeper Jose Sa and Saiss allowed the Portuguese international to walk the ball towards an unguarded net, but he fired straight at Conor Coady on the line rather than placing the ball into the corner.
Heroics from Sa then seemed set to earn Wolves a point as he denied Mane and Salah.
But he was finally beaten with virtually the last kick of the game as this time Salah played the provider and picked out Origi, who spun before lashing the ball in low on his left foot to spark scenes of wild celebration from Klopp and the rest of the Liverpool bench.