Jamie Vardy put Leicester ahead but Liverpool, who had new £75 million ($100 million) signing Vigil van Dijk watching from the Anfield stands, fought back after the interval to secure the points.
Salah was again instrumental for Jurgen Klopp’s side as he took his tally to 17 Premier League goals this season with two fine finishes.
Liverpool, who remain fourth, are four points clear of fifth placed Tottenham.
Klopp’s goalkeeper rotation policy saw Loris Karius start ahead of Simon Mignolet, who dropped to the bench, and after just three minutes the German was forced to pick the ball out of the net.
Joel Matip’s timid pass from the back sold Emre Can short and Vicente Iborra’s sharpness saw him steal possession and quickly release Riyad Mahrez down the right flank.
The Algeria winger glided past left-back Andrew Robertson and his teasing low cross was met by Vardy, who showed his penalty box predatory instincts to nip in front of Matip and finish.
It was Vardy’s 10th goal of the season in all competitions as he again scored against a top-six club having netted previously in matches against Arsenal, Chelsea, Tottenham and both Manchester clubs.
Liverpool shook off their sluggishness and should have equalised moments after Vardy’s opener when Salah was found by Sadio Mane only to get his angles wrong and drag a shot wide from eight yards.
Philippe Coutinho stung the palms of Kasper Schmeichel with a long-range effort while Mane had the ball in the net from Robertson’s cross only to be correctly flagged offside.
Liverpool continued to threaten the visitors’ goal from distance with Joe Gomez and Roberto Firm THINK YOUR FRIEND WOULD BE INTRESTED? SHARE THIS STORY USING ANY OF THE SHARE BUTTON BELOW ⬇ PLACE YOUR TEXT ADVERT BELOW:>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ( FREE ) secret Fruits that Increased My Manhood size and Lasting Power in 7-days... CLICK HERE TO GET IT Warning To Men: This 3 Foods Is Killing Your Erection. Click Here To Know Them