Salah won the Group E match for Liverpool with his second of the night in the 69th minute, denying Salzburg a point after teenage sensation Erling Braut Haaland had stunned the Reds when he completed an incredible fightback with his 18th goal of the season.
The hosts looked to be cruising when Egyptian Salah had added to goals by Sadio Mane and Andy Robertson with a neat finish in the 36th minute, but Hee-Chan Hwang’s brilliant strike shortly before the break gave Salzburg hope.
Two goals in four second-half minutes from Takumi Minamino and 19-year-old substitute Haaland, who had only been on the pitch for four minutes when he evaded a dozing Liverpool defence to tap in Minamino’s low cross, left the home crowd stunned.
However, Salah spoiled their evening with his sixth goal of the season in all competitions, putting Liverpool level with Salzburg on three points, one behind Napoli after their disappointing goalless draw at Genk.
Suarez saved Barcelona’s blushes at the Camp Nou after Lautaro Martinez had scored early for Inter, who then failed to capitalise on their first-half dominance in the Group F clash and lost 2-1.
Marc-Andre ter Stegen had to be at his best in the 37th minute to get down low and keep out Martinez’s powerful header, while Stefano Sensi also rued missing the target when well placed shortly afterwards.
However Barca moved up a gear in the second half and were deservedly level when Suarez crashed home a superb shot just before the hour mark, and the Uruguayan was at his sharpest to win the match with six minutes remaining.
Lionel Messi, a surprise inclusion from the start, suddenly warmed up and skipped past two challenges before laying on Suarez, whose perfect first touch allowed him to sink Inter and draw Barca level on four points with group leaders Borussia Dortmund.
– Flamboyant Ajax shine again –
The Bundesliga outfit came out on top at Slavia Prague thanks to a pair of counter-attacking strikes from Achraf Hakimi, whose clinical finishing led Lucien Favre’s side to a 2-0 win in the Czech Republic.
The Morocco international burst through onto Julian Brandt’s pass in the 35th minute and charged towards the goal, skipping past Petr Sevcik and goalkeeper Ondrej Kolar before rifling home the opener.