The Merseysiders had pulled back from a two-goal first leg deficit to take the second leg into extra time. Neither side could break the deadlock and it then went to a penalty shootout.
Ryan Taylor missed with the first effort for Tranmere, which was saved by Dimitrios Konstantopoulos, but Paul Hall, Gareth Roberts, Iain Hume, Chris Dagnall and David Beresford went on to score. Mark Tinkler saw Hartlepool's second effort saved but Gavin Strachan, Joel Porter, Matty Robson, Chris Westwood and Anthony Sweeney found the target.
Ian Sharps took the seventh Rovers kick and saw his effort palmed away by the keeper and Richie Humphreys stepped up to coolly find the target for a 6-5 shootout victory.
Tranmere dominated the second leg although it was not until the 87th minute that they managed to get level.
John Achterberg did not have a save to make in the home goal before half time, as Westwood headed over with the only Hartlepool effort from a Strachan corner.
At the other end Jason McAteer saw a 20 yarder saved easily but there was luck on the keeper's side in the 12th minute. He was beaten by an angled shot from Hume but the ball cannoned off the crossbar, before a snap shot by Roberts was deflected into the side netting.
There was a blow for Rovers when skipper McAteer was forced off in the 20th minute to be replaced by Danny Harrison.
Konstantopoulos brought off a fine save to deny Eugene Dadi in the 24th minute and again denied the striker in first-half injury-time by turning a header on to the crossbar.
Harrison blasted over from the edge of the box early in the second period and the United keeper made good saves from headers by Hall and Michael Jackson.
Hartlepool lost skipper Michael Barron through injury after 66 minutes with Tinkler taking over.
The home side broke through in the 70th minute after Hume was fouled just outside the box and Taylor's well-struck free-kick found the target.
Taylor then fired well over and put two more free-kicks from dangerous positions into the wall.
As Tranmere maintained their pressure, a Dadi header flashed just outside a post.
But it was finally 2-0 and 2-2 on aggregate in the 87th minute with substitute Beresford blasting home a low drive from 20 yards after good work by Hall.
Both sides tired in extra-time but Konstantopoulos made a fine save to deny Hume in the 112th minute. At the other end, Porter failed with an angled effort after a Thomas Butler shot was blocked.
Robson was outstanding for Hartlepool but there was also some terrific work in central defence by Michael Nelson and Westwood.
The result was certainly harsh on Tranmere for whom Hall, Hume and Taylor worked tirelessly.