Salah scored his hat-trick in 6 min
Salah entered the substitute in the 68th minute and scored his hat-trick in the 75th, 80th, and 81st minutes, i.e., in a span of six minutes and 12 seconds.
The Brazilian Roberto Firmino scored a double in the 24th and 55th minutes, while the other two goals were scored by Uruguayan Darwin Nunes (66) and Harvey Elliott (87).
Liverpool compensated for its fall against its host Arsenal 2-3 Saturday in the league and confirmed its readiness for the upcoming summit at home Sunday against Manchester City, and also continued its continental awakening with a third successive victory.
And the German coach of Liverpool, Jurgen Klopp, kept the stars Salah, the Spaniard Thiago Alcantara, and the Portuguese Diogo Jota on the bench.
Rangers had the advantage at the beginning of the match and translated it into an early goal scored by Canadian Scott Arfield when he received a ball from Jack Ryan at the edge of the area and hit it crawling to the right of Brazilian goalkeeper Alison Becker (17).
This is the first goal for Rangers in the group stage this season.
But the joy of the hosts did not last only seven minutes, as Liverpool managed to equalize when Greek defender Konstantinos Tsimikas kicked a corner kick that Brazilian Roberto Firmino headed into the goal (24).
Firmino gave Liverpool the lead at the beginning of the second half when he received a cross on a plate inside the area from right defender Joe Gomez, and the Brazilian followed it with his left hand from a close range between the legs of goalkeeper Alan McGregor (55).
Nunes reassured the Liverpool fans by scoring the third goal with a right-footed shot from inside the area after a superb pass from Firmino (66).
Immediately after the goal, Klopp pushed Tiago, Salah, and Scottish Andrew Robertson in the place of Jordan Henderson, Nunes, and Tsimikas.
Salah strengthened Liverpool's progress when he took advantage of a rebound from one of the defenders inside the area, with a powerful shot into the goal (75).
Salah added the fifth with a shot from the edge of the area after a pass from the other substitute Jota (80), before achieving the hat-trick with a deceptive shot from inside the area to the right of McGregor after a pass from Jota also (82).
Harvey Elliott sealed the festival with a seventh goal with a shot from close range following a rebound from McGregor (87).
Liverpool is in second place with 9 points, behind the leaders Napoli with 12 points, while Rangers are the last without any points.