Salah ran the length of the opposition half to slot a finish into the right corner on 80 minutes and Henderson tucked the third home six minutes later to settle another hard-fought result for Jürgen Klopp’s team.
Shane Long had opened the scoring for Saints in the ninth minute with a clinical, low drive past Alisson Becker, but Naby Keita’s first goal for the Reds restored parity before the break.
The final score meant Liverpool moved back above Manchester City at the top, two points clear having played one match more than the reigning champions.
Team news
Klopp made two changes to the side that started last weekend’s win over Tottenham Hotspur, with Fabinho and Keita brought into the XI in place of Henderson and James Milner.