It was a thrilling end-to-end affair with Tranmere playing well above their recent home form.
Twice the Merseysiders held the advantage but in the end a draw was a fair outcome.
Tranmere dominated for much of the first half and Gareth Roberts struck the crossbar after only seven minutes.
But Rovers went ahead in the 18th minute with a debut goal from loan signing Simon Francis. He picked up a part clearance and beat keeper Willy Gueret with an angled shot from the edge of the box.
It was against the run of play when Swansea drew level in the 45th minute after a free-kick by Lee Trundle rebounded off the defensive wall.
The ball ran to Kevin McLeod who crossed for Owain Tudur-Jones to power home a superb header.
But Tranmere rocked Swansea as they regained the lead in first-half injury time.
Sam Aiston powered the ball forward from defence and Chris Greenacre was the link to send Delroy Facey clear.
Facey finished stylishly past the on-rushing Gueret.
Swansea sent on Andy Robinson and Roberto Martinez immediately after the break and they began to look much more dangerous.
But Tranmere stuck doggedly to their task and Facey missed two great chances to make the game safe.
With two minutes remaining, home keeper John Achterberg could not hold on to a shot from Adebayo Akinfenwa and Robinson was on hand to net from close range against his home town club.
City almost sneaked it in the dying seconds but a shot from Izzy Iriekpen hit a post.