Swansea boss Michael Laudrup, with next Sunday's Capital One Cup final in mind, made seven changes to his side and the Reds took full advantage, with Suarez outstanding.
Suarez won a 34th-minute penalty following Kemy Agustien's unnecessary challenge. Steven Gerrard, having failed from the spot in front of the Kop against West Brom earlier in the week, went for the opposite corner and succeeded in beating Michel Vorm.
The Reds' lead was doubled just 16 seconds after the break when new signing Coutinho skipped through the Swans defence and slotted home after an incisive pass from Suarez.
Four minutes later and Jose Enrique put the game to bed following a great team passing move, finishing after a slick one-two with Daniel Sturridge.
Suarez finally got the goal his play deserved on 56 minutes when he went past both Swansea's centre-backs following a Stewart Downing assist.
Sturridge added a fifth from the penalty spot with 19 minutes to play after the ball hit substitute Wayne Routledge in the box.
The Liverpool striker almost added a sixth but hit the bar with his placed effort from just inside the box.
At the other end Pepe Reina saved to his left to deny Routledge a consolation for the Swans.
Liverpool's day was marred late on when substitute Fabio Borini, who had come on for Suarez, suffered a suspected dislocated shoulder following a challenge. He was forced to leave the field and the Reds, who had used all their substitutes, finished the game with ten men.
The win was a welcome boost after a five-match winless run in all competitions and moves the Reds to within nine points of fourth-placed Tottenham.