The Reds kicked off the weekend schedule knowing they went winless in six Saturday 12.30pm kick-offs last season, and that run looked likely to continue until captain-for-the-day Andy Robertson scored four minutes from time. Hugo Bueno deflected Harvey Elliott’s shot past Jose Sa for a third in added time.
The hosts dominated the first half at Molineux against an unusually sloppy Liverpool, with Hwang Hee-chan stroking in a 7th minute goal after a brilliant run from Pedro Neto, before Wolves missed a string of further chances.
Wearing the captain's armband on his 200th Premier League appearance, Andy Robertson slid in Liverpool's second from another Salah pass in the 85th minute as the visitors poured forward.
Liverpool made it three in time added on, with Wolves' Hugo Bueno touching the ball into his own net from a shot by Harvey Elliott, sending the away fans into delirium.
The result put Liverpool top of the table for now on 13 points after five games. Wolves are 15th on three points.
Additional reporting by Reuters.