The Reds started the better of the two outfits on Merseyside as Cody Gakpo enjoyed a newfound relationship with Andrew Robertson on the left flank.
But a howler by Alisson in the 26th minute gifted Goncalo Guedes a chance to take the lead, following a number of defensive errors by Liverpool.
Ibrahima Konate stood out in the Reds' back line for the wrong reasons in the early staged, a diamond in the rough, as Wolves continued to impose after scoring.
Despite Liverpool dominating possession of the ball in the first-half, the visitors generally found more joy with it.
Just before the break, though, Darwin Nunez expertly latched onto a deep Trent Alexander-Arnold cross to level the score-line.
Mohamed Salah put Liverpool 2-1 up shortly after the break, placed well to score on the rebound via a loose balll in the 52nd minute.
The Reds made good on their improved performance in the second period, but their visitors defended well in equal measure.
And Wolves made even better on their sturdiness, carving out a chance to attack, levelling the score-line at 2-2 through super-sub Hwang Hee-chan in the 67th minute.
Anfield's visitors thought they'd snatched the match from Liverpool through Toti Gomes in the 81st minute, but the goal was ruled out for offside.
Frustration grew on both sides, but a stalemate is what was eventually settled on. A replay will now take place at the Molineux.
