Roberto Firmino gave the hosts the lead with a straight shot on goal in the 20th minute, delivered to the Brazilian striker by Andrew Robertson's cross from the left flank and built up from Xherdan Shaqiri's through ball.

The Serbian league champions had a couple early scoring chances but Liverpool quickly settled into their attacking rhythm peppered with some pinpoint long passes to Salah.

Liverpool doubled the lead right before half-time when Salah scored his first on the night with a strike to the near post, set up once again by Shaqiri on a quick tap from just outside of the box.

After the break, Salah made it a half-century worth of goals for Liverpool when he buried a penalty shot in the 51st minute after Sadio Mane drew the foul off Red Star captain Filip Stojkovic.

One of the visitors' few bright spots on the night was Milan Borjan's save of Sadio Mane's penalty shot in the 76th minute. The Canada international managed to deflect enough of the ball off the bottom side of the crossbar and deny Mane's second chance for the score.

Mane would redeem himself four minutes later, adding Liverpool's fourth on the night off a right-footed shot from the center of the box to the bottom left corner.

Liverpool moves to the top of the group with six points after three matches. Napoli, who drew with Paris Saint-Germain on Wednesday, slipped to second with five points. The French side stays in third place with four points, and Red Star remains at the bottom with one point.