Alexis Sanchez was dropped to the bench as Olivier Giroud lead the line, but it mattered little as the Reds ran riot with Roberto Firmino and Sadio Mane putting them two goals to the good at half-time.
Sanchez was introduced at the break, and created Danny Welbeck's goal, but Georginio Wijnaldum wrapped up the three points in injury time.
In the early kick-off, Manchester United missed the chance to boost their own top-four chances as they drew 1-1 at home with Bournemouth.
Premier League table
Marcos Rojo gave United an early lead at Old Trafford, but United academy graduate Josh King equalised from the penalty spot.
Controversy reigned as Tyrone Mings and Zlatan Ibrahimovic both avoided red cards just before the interval - the former for a stamp on the striker; the latter for elbowing the defender in retaliation - as Bournemouth midfielder Andrew Surman then received a second bookable offence for pushing over Ibrahimovic.
The Swedish striker was lucky to be on the pitch, but then missed a second-half penalty as Jose Mourinho's side failed to break down Eddie Howe's Cherries.
The result was a boost for both Arsenal and Liverpool as they face off at Anfield later on Saturday afternoon, with third-placed Tottenham hosting Everton on Sunday before leaders Chelsea travel to West Ham on Monday night.
Crystal Palace secured a vital 2-0 victory against West Brom at The Hawthorns to move three points clear of the relegation zone.
Goals from Wilfried Zaha and Andros Townsend were vital for the Eagles with relegation rivals Swansea and Leicester also winning on Saturday.