Liverpool maintained the pressure in the race for Champions League qualification as Jordan Henderson's fortunate second-half goal saw off Swansea at the Liberty Stadium to seal a 1-0 win.
Henderson's 68th minute winner - his sixth goal of the season and his third in successive Premier League games - had a slice of good fortune about it as Jordi Amat's attempted clearance clattered into him, but Liverpool will not worry about that on a night when Swansea had them clinging on for large parts of the first half.
But Liverpool showed the resilience of a side which has not conceded away from home in the league since December 14 and grew in stature as the second half unfolded.
The gap between themselves and fourth-placed Manchester United was cut to two points again before the pair meet in a huge Anfield collision on Sunday.
After Arsenal and United both won over the weekend Liverpool knew they could not afford slipping up in south Wales and they were boosted by the return of skipper Steven Gerrard to the matchday squad after missing seven games with hamstring trouble.
But Gerrard started on the bench as Rodgers kept faith with the midfield and attacking personnel which has had served him so well in recent weeks and underpinned the performances which have made Liverpool the form team of 2015.
Joe Allen had shaken off a hip injury to feature against his former club and Martin Skrtel had recovered from the sickening fall which forced his withdrawal from Liverpool's last game, the FA Cup quarter-final tie against Blackburn eight days earlier.
Bafetimbi Gomis had also been declared fit to lead the Swansea forward line after collapsing on the field at Tottenham on March 4, the result of a vasovagal condition which can lead to low blood pressure but one which apparently has no lasting effects.
Liverpool's need for the three points was greater than a Swansea side who had already reached the 40-point mark expected to guarantee another season of Premier League football, but it was the hosts who enjoyed the greater possession and scoring opportunities in an enthralling first half.
Swansea were also slick on the break and Allen's saving tackle prevented Gomis from profiting after rounding Emre Can before Skrtel took up the right position to clear Ki Sung-yueng's header at the back post.
Skrtel's carbon-copy clearance soon denied Gomis as Swansea spotted a route to goal through Wayne Routledge's forays down the right flank and crosses to the far post.
Liverpool offered only fleeting moments of menace, most notably when Daniel Sturridge held off Amat for Adam Lallana to fire into Lukasz Fabiasnki's midriff and the Polish goalkeeper comfortably plucking Philippe Coutinho's 20-yard shot out of the air.
But it was Swansea's one-touch passing which was catching the eye and Ki found Gomis whose smart one-two with Routledge freed the Frenchman on goal.
Gomis took the shot early, maybe too hastily, but it still forced a fine sprawling save from Simon Mignolet in the Liverpool goal.
Mignolet made an even better save from Gylfi Sigurdsson's curling effort and was then relieved to see Jonjo Shelvey's strike from the resulting corner deflect to safety off Alberto Moreno.
Rodgers must have demanded a major improvement from his side at the start of a second half which opened with Gomis arriving late after the action had started.
And Liverpool immediately began to find their rhythm, if not the final ball, as Swansea were penned back in their own half for the first time in the match.
Swansea were almost cut open after 58 minutes when Sturridge fed Raheem Sterling down the right and his cut-back found Coutinho who forced an excellent save from Fabianski at the base of his post.
Gerrard was sent on after 64 minutes with Liverpool firmly in the ascendancy and he was soon celebrating a goal, even if it came in rather fortuitous fashion.
Skrtel advanced from the back and his pass squirmed through off Sturridge before Amat's attempted clearance cannoned off Henderson and over the helpless Fabianski.
After that Liverpool pretty much held Swansea at arms length and Sturridge almost put the gloss on the win when he struck the post in injury time.