Ronnie Moore named an unchanged side from the one which beat Chesterfield 2-0 eight days ago, although Danny Harrison replaced the injured Jason McAteer on the bench, who was missed in midfield.
The game started well for Swansea, who's support of just 494 fans had something to shout about after four minutes as a Gavin Ward clearance rebounded off Lee Trundle but Ian Goodison was on hand to head the ball back to his 'keeper.
Just two minutes later, The Jacks took the lead through Tranmere old boy Andy Robinson who netted at Prenton Park for the second season running.
Leon Britton, standing at just 5.06 tall, drifted down the right wing before floating a cross into the area where Robinson was able to pounce near the penalty spot to head past Ward.
Ian Craney nearly double the lead five minutes later as his long range effort swerved and bounced in front of Ward who could only unconvincingly push the ball round the post before Rovers had their first chance of the game on 13 minutes as Paul McLaren blasted his shot well over the bar and into the Cowshed.
On 22-minutes, Chris Shuker registered Tranmere's first shot on target, more surprisingly with a header, as his flick on almost crept under Willy Gueret's cross-bar but the tall goalkeeper was able to keep the ball out.
On 26-minutes the ball was back in the Tranmere half as Ward saved from Britton's volley whilst Robinson and Trundle both had further efforts in the next few minutes.
With two minutes of the half remaining, Tranmere inside the Swansea half with a free-kick 25-yards from goal. The set-piece was taken by Shuker, whose curling effort was saved by Gueret near his post and this proved to be just about Rovers last shot on target as Ellison headed wide soon after.
The second half started fantastically for Swansea, as Robinson first hit the post on 49-minutes before Lee Trundle doubled The Jacks lead on 52-minutes.
Trundle beat the offside trap and broke down the Tranmere right and after steaming into the penalty area, leaving Chris McCready in his wake, shot across Gavin Ward and into the net.
However, to somewhat sour the mood Trundle was booked for "over-celebrating" in front of the Tranmere fans in the Borough Road Stand.
Swansea were on the attack again just four minutes later as Gavin Ward was forced into another save from Andy Robinson.
On 59-minutes, much to the delight of the Tranmere fans, Trundle was given a second yellow card, followed by a red, as he kicked the ball away after the referee had blown his whistle.
It did take Trundle about five minutes to leave the pitch but this allowed fans to get a good look at the 29-year old scouser, and it must be said that he has a great tan for somebody living in Swansea, not particularly famed for it's good weather.
On 62-minutes, Tranmere and Ronnie Moore looked to put pressure on Swansea as they switched to a 3-4-3 formation, replacing Shane Sherriff with Calvin Zola who went into attack.
Five minutes later, Robbie Stockdale shot well wide and over into the Kop from just inside the Swansea penalty area as Tranmere pushed forward looking for a repeat of the result against Cheltenham at Prenton Park almost two weeks ago.
On 70 minutes Chris McCready headed wide from a Shuker cross and the central-defender should have had a penalty minutes later as he was bundled down in the area by Dennis Laurence, but referee Mr. G. Laws only gave Tranmere a corner.
Gareth Taylor had a perfect chance to head Tranmere back in the game minutes later as he connected with a John Mullin cross but headed just wide whilst Kevin Ellison was replaced by Steve Davies on 82-minutes.
The last action of the game saw Gueret in the Swansea goal pull off a wonder save from John Mullin, who drove the ball towards the roof of the Swansea goal from close range but Gueret palmed the ball out for a corner.
This report makes it sound as if the game was being played in the Swansea half for the second 45-minutes. However, this is far from the truth as Rovers showed little passion or urgency in searching for a win. Anybody would have thought they didn't want to go up as they blew the chance to go another two-points clear of Blackpool and seven clear of their opposition for the day.
Jones' Man Of The Match: For me, despite being subsituted, Kevin Ellison was one of Rovers better players on the day, but the man of the match for me was the only other player who showed any passion and will to win - Robbie Stockdale. The Scotland international made some key tackles and did his best getting forward but it is a team game and unfortunatly Stockdale and Ellison didn't have the other nine players with them today.