He struck in the 30th minute with a far post header from a Lee Trundle cross after all the early running had been done by the visitors.
Both sides managed to miss from the spot in the first half and although Tranmere had most of the possession they rarely carved out any clear goalscoring opportunities.
Swansea attacked straight from the kick-off and a Trundle shot was cleared off the line by Paul Linwood after John Achterberg had failed to gather an Adrian Forbes cross.
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Rovers struck back when skipper Jason McAteer slipped a pass wide to Gareth Roberts but his first-time shot flew well wide of the far post.
Rovers settled down with Calvin Zola a lively front runner and McAteer pulling the strings from midfield and the home defence were at full stretch for long periods.
Against the run of play on the half hour the Swans took the lead when Trundle lifted a cross from the right over the keeper's outstretched hands to Akinfenwa who was waiting at the far post to head home.
The busy Zola then sped into the Swansea area in the 39th minute where he was brought down by Sam Ricketts but Willy Gueret dived to his right to push McAteer's spot-kick away.
Right on half time the roles were reversed and Ian Sharps brought Trundle down in the box and when Trundle himself took the spot-kick it was a weak attempt and Achterberg had plenty of time to gather to his left.
Rovers began the second half forcing the Swans back and Gueret was called into action to punch clear from Zola.
In the 52nd minute the French keeper had to leap to his right to turn over a Chris Greenacre shot destined for the top corner.
Rovers were clearly frustrated at not being able to open up the home defence and after an hour manager Brian Little made all three changes together in an attempt to gee up his side.
Tranmere continued to have most of the possession but with Gueret in superb form they were unable to make it count despite camping in the Swansea half for long periods.
In a frantic last five minutes the visitors peppered the Swansea goal yet the clearest scoring opportunities went the home side's way with Trundle and Forbes both going close after breakaways.