Goals from Diogo Jota, Darwin Nunez and Salah gave Liverpool a comfortable 3-0 win over Nottingham Forest at Anfield on Sunday that lifted the Reds to 23 points, three behind leaders Tottenham Hotspur.
Forest came to pack their defence and hit on the break, and though they kept it tight for the opening half-hour, they were soon behind thanks to a classic counter-attack from the home side.
Forest centre-back Murillo made an ill-judged foray forward and was relieved of the ball, and in seconds Mohamed Salah had found Nunez, whose shot was parried into the path of Jota for an easy finish.
Jota celebrated by holding up the shirt of teammate Luis Diaz, who missed the game following the kidnapping of his parents in his native Colombia.
"Luis was with us in the hotel, then he went home. It's a very hard situation and I don't know how anyone would react if it happened to you," Jota told the BBC.
"He was going to play. I played instead of him and I showed him his shirt to show we're with him and we hope everything works out."
Liverpool's second was a brilliant team goal as they sliced the Forest rearguard, and this time it was Dominik Szoboszlai who got free down the right to pull the ball across the goal for Nunez to score.
Liverpool upped the tempo early in the second half with Salah curling a shot just wide and Harvey Elliott having a shot blocked shortly after coming off the bench.
A breakdown in communications between substitute Harry Toffolo and keeper Matt Turner let Salah in, and he duly steered the ball home to complete the scoring in the 77th minute.
Forest never got out of their defensive mindset and it took them until the 85th minute to register their best effort of the game, a shot by winger Anthony Elanga that cannoned off the underside of the crossbar.
The defeat leaves Forest in 16th place in the table on 10 points, five points above the drop zone, while Liverpool are still in the mix at the top of the table after a difficult day off the pitch caused by Diaz's family situation.
"The preparation was the most difficult I had in my life. Didn't expect it, couldn't prepare for it, We try to help 'Lucho' (Luis Diaz) as much as we can," Liverpool manager Jurgen Klopp told reporters.
"I told the boys after the game that the best thing I can say is we played really well, and there's still so much space for improvement."