The past week had been "a bumpy road" in the Liverpool reign of Brendan Rodgers but respite was waiting at the end in the form of a compliant old friend. Swansea City would only have looked more in cup final mode had they played at Anfield in new suits and broken off to record a song. Liverpool capitalised ruthlessly to leave Michael Laudrup fearing the impact at Wembley on Sunday.

Rodgers, the former Swansea manager, denied harbouring any pre-match worry over the reaction to a sixth game without a win for Liverpool. Recent performances, however, littered with wasteful finishing and weak defending, have undermined not only the club's aspirations for the season but faith in the manager's ability to realise them. The rout, Liverpool's first win since the 5-0 defeat of Norwich City on 19 January, was therefore timed to perfection. The mitigating factor of Swansea's weakened team before their Wembley date with Bradford City was of no concern to Rodgers.

Luis Suárez inspired the performance, aided and abetted by the January recruits Daniel Sturridge and Philippe Coutinho. The new signings are ineligible for Thursday's Europa League second leg against Zenit St Petersburg but Liverpool have at least trained their sights as they attempt to overturn a 2-0 deficit.

Rodgers said: "It has been a bumpy road this week but it was important we showed mental toughness and kept a clean sheet. We have not been at our best defensively in the last four games." The one downside was the dislocated shoulder that is expected to end Fabio Borini's season.

The question of how much a distraction the League Cup final would be to Swansea was answered with the arrival of the team sheets. Laudrup made seven changes to the side who beat QPR in their last Premier League outing, when they lost Chico Flores to an ankle ligament injury, and the no-risk policy meant a place on the bench for their captain, Ashley Williams, and their leading goalscorer Michu. The visitors' threat disappeared with him. His replacement, Itay Shechter, lacked support and strength on the ball to seriously trouble the Liverpool defence.

With Swansea minds elsewhere and Liverpool playing on the back of successive 2-0 defeats, the game had a subdued, end-of-season air. It had a restorative effect on Liverpool's confidence in front of goal, however.

After an initial flurry when Jamie Carragher prevented Shechter reaching Roland Lamah's pass to the near post and Lamah, making his first league start, had an optimistic penalty appeal against Glen Johnson rightly refused, the visitors created nothing in the final third. Liverpool peppered Michel Vorm's goal with shots, although, despite Swansea's disintegration and the final scoreline, it was only after Kemy Agustien committed a needless foul on Suárez in the area on 34 minutes that they convinced in attack. Rodgers' team had 11 shots in the opening 20 minutes, with one on target.

Johnson headed wide from Stewart Downing's inviting cross, Suárez shot over, Sturridge went close from another Downing delivery and Anfield lambasted the referee Howard Webb for denying Sturridge a penalty when the striker stumbled over Kyle Bartley's leg. Webb played a good advantage instead, but the full debutant Coutinho shot wide from six yards. The young Brazilian otherwise enjoyed a productive and promising afternoon.

Then came Agustien's challenge on Suárez as the Liverpool striker retrieved a Steven Gerrard corner at the back of the area and cut to the byline. The contest changed irrevocably. The ball was almost out of play when the Swansea midfielder tripped Suárez and, with Webb unsighted, the assistant referee Mike Mullarkey signalled for a spot-kick. Gerrard made amends for his penalty miss against West Bromwich Albion last Monday by beating Vorm low to the goalkeeper's right and Swansea's chances were as good as over.

Only 20 seconds had gone in the second half when Suárez released Coutinho with a fine pass. The £8.5m acquisition advanced on Garry Monk, twisted him inside and out, and shot through Vorm's weak guard to mark his full debut in style. A flowing move down the Liverpool left ended with José Enrique converting Sturridge's ball across the box, Suárez scored a fine goal when he collected Gerrard's pass, beat two defenders and found the bottom corner and Sturridge scored Liverpool's second penalty following a deliberate handball by the Swansea substitute Wayne Routledge.

The watching Bradford City manager, Phil Parkinson, had seen enough and left his seat in the directors' box. He can only hope the rout will prey on Swansea minds on Sunday.

Man of the match Luis Suárez (Liverpool)