It looked as though Trent Alexander-Arnold had given Liverpool an early lead when Diogo Dalot was unable to clear his attempt off the line, but the Red Devils were saved due to Salah being offside before touching the ball to his right-back.
That epitomised the breathless start to proceedings with both sides keen to take the front foot in such a vital fixture.
The hosts had the better of the early possession but lost the ball in dangerous areas - even if they initially recovered well enough to remain level.
Liverpool took the ascendancy as the half-hour mark came and went, but had a precarious moment of their own that culminated in Noussair Mazraoui’s fizzing effort being saved by Alisson.
The visitors eventually got their opener in the 35th minute when Casemiro’s wasteful pass was capitalised on, with Ryan Gravenberch striding forward and offloading the ball to Salah, whose dinked cross was headed home by Luis Diaz.
There was further punishment just seven minutes later, as Díaz stole the ball from Casemiro before laying it off to Salah and getting it back via an exceptional outside-of-the-boot cross to apply a clinical first-time finish.
Toby Collyer replaced Casemiro at half-time for his Premier League debut and was quickly involved, nodding the ball down for a Joshua Zirkzee effort that was palmed away by Alisson.
The Red Devils’ problems persisted, though, as Kobbie Mainoo was outmuscled by Alexis Mac Allister, who sprung a counter that culminated in a typically cool finish from Salah.
The Egyptian, who has now scored in his last seven appearances at Old Trafford, came close with two more efforts as boos rang out around Old Trafford.
While things didn’t get any worse for the Red Devils, there was no lift with Alisson denying Zirkzee’s close-range header before the Dutchman sent another attempt wide.
Liverpool therefore maintained their perfect start to the season while also beginning a Premier League campaign with three clean sheets for just the third time ever.
In contrast, United have now suffered back-to-back defeats, piling the pressure on manager Erik ten Hag going into the international break.
Flashscore Man of the Match: Mohamed Salah (Liverpool)
Check out the match stats here.