The Giallorossi leapfrogged their rivals to move second in the Serie A table with the three points, a victory that was wrapped up when Salah found the bottom corner five minutes from time.
Edin Dzeko had earlier scored twice to give Luciano Spalletti's men the advantage.
“It was really important to win today because it takes us above Napoli," Salah said. "Now we need to keep playing this well.
"We have a great team with great players and we want to win something."
Salah had praise for fellow goalscorer Dzeko, as the two men once again both appeared on a scoresheet.
“He's a fantastic player and I like playing on the same team as him in training," Salah added. "He's got off to a superb start this year – he's already scored seven.
"He's a key player for us.”
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