Both teams looked good and sharp on the break and stand-in Liverpool goalkeeper Caoimhin Kelleher was forced to scramble to his right to keep out a cute chipped effort from Daniel Podence.
But the 2,000 home fans inside Anfield — allowed into the stadium after coronavirus restrictions were eased in certain parts of England — had something to cheer in the 24th minute.
There did not appear to be much danger when Liverpool captain Jordan Henderson sent a long ball over the top into the Wolves penalty area.
But Coady, who used to be on Liverpool’s books, got his calculations wrong. The ball came off his chest and Salah nipped in to fire home left-footed.
Wolves were awarded a penalty in the dying minutes of the first half after Mane was adjudged to have fouled Coady.
But VAR ruled out the spot-kick after the TV replay showed there had been no contact.
Wolves searched for a way back into the match in the early stages of the second half and Coady found himself in a threatening position in the Liverpool box before Fabinho whipped the ball away.
Seconds later, Liverpool were charging forward again on the counter-attack, towards the Klop.
Henderson played a long ball which Wijnaldum collected before producing a measured finish into the top left-hand corner of Rui Patricio’s net.
Liverpool put the result beyond doubt in the 67th minute when Salah’s inswinging cross was met by Joel Matip from close range.
By now the home side were in total control, with Salah trying to dance his way through Wolves defenders.
Liverpool’s fourth goal came when substitute Trent Alexander-Arnold, returning from injury, produced a delicious cross from the right which was turned in by Nelson Semedo for an own goal.