The visitors could afford the luxury of making nine changes from their New Year's Day draw against QPR - bringing in six players aged 23 or under - and still progress relatively untroubled against a side fighting for their Football League status 80 places below them.
Their first three goals from Nathan Dyer, on-loan Tottenham midfielder Tom Carroll and Gambian youngster Mo Barrow - the latter two with their first for the club - were all tinged with touches of Premier League class.
Max Power fortuitously benefited from charging down Swansea goalkeeper Gerhard Tremmel's clearance before Bafetimbi Gomis (twice) and substitute Wayne Routledge - either side of Cole Stockton's header - ensured there was no dramatic turnaround.
Swansea spent the majority of the first half in control, passing the ball about without actually looking like they would punish their hosts.
In Gomis and Marvin Emnes they had a front two with the experience and ability to cut through a League Two defence but it took a while for them to work that out
Once they did they made the difference.
Wales goalkeeper Owain Fon Williams' reflexes tipped over Gomis' instinctive close-range shot, Swansea's first genuine attempt, although Tranmere were fortunate to escape when the unmarked Jay Fulton completely missed his kick at the far post.
Emnes drove wide from distance before a real touch of class and a silky touch from Dyer saw him glide through the defence and convert the rebound from his blocked shot, although not without Tranmere appealing for use of a hand.
That finally sparked the hosts into life and they showed much more ambition and creativity in the final 10 minutes of the half.
Their best chance saw Power's effort saved at the second attempt by Tremmel after the 20-year-old Fulton, on only his fifth appearance for the club, gave the ball away and then compounded a disappointing afternoon by getting booked minutes later.
Swansea's second just after the break deflated Tranmere's renewed optimism as Barrow knocked the ball inside for Carroll to cleverly skip past a lunging challenge and clip home.
The visitors' third, when Barrow side-footed home from Gomis' cross, wrapped up the result with more than half-an-hour to go.
On-loan Aston Villa defender Janoi Donacien beat Tremmel but not the post and Rovers could not force home the ensuing goalmouth scramble, although Tremmell was embarrassed with 20 minutes to go when he drilled a clearance straight at Power and watched the ball fly past him into the net.
The Emnes-Gomis partnership extinguished any fanciful hopes of a glorious finale when the latter drilled home 13 minutes from time but Stockton's 83rd-minute effort restored some pride before Routledge and Gomis, again, struck.
Source : PA
Source: PA