Jurgen Klopp named the same starting line-up that did duty against RB Leipzig in the UEFA Champions League last 16 second-leg last Wednesday.
Liverpool were cut open in the earlier minutes when a forceful move from Adama Traore prompted the overlapping Nelson Semedo to work goalkeeper Alisson Becker into a save.
Following the nervy start, Liverpool should've gone ahead on 12 minutes after Sadio Mane ran through the centre of the defence for a simple finish but Rui Patricio recovered to thwart.
Mane was presented another chance after the half-hour mark through a teasing ball at the near post of the area by Trent Alexander-Arnold, but the former headed wide of the bottom-corner.
Wolves were breached with the last kick of the first half from a first-time shot on the inside of the area by Diogo Jota, with Patricio's outstretched arm unable to keep out his former teammate.
Nuno Espirito Santo's side emerged for the second half buoyant following a header in the area from Conor Coady, but he went off target.
Liverpool contained the home side's relentless pressure towards the midway stage of the second half and nearly had a second from a looping header by Fabinho following a free-kick.
This signalled a double substitution from Klopp a little later, as Georginio Wijnaldum made way for James Milner with Thiago Alcantara withdrawn for Naby Keita.
As Wolves attempted a strong finish, the Reds netted again from a tight angle by Salah but the flag went up as a lengthy stoppage saw Patricio stretchered off for John Ruddy, however 1-0 it finished.
