Teenage striker Chris Dagnall was sent off in the 68th minute for over celebration after he scored the winning goal.
Dagnall, 18, had already been booked in the first period for a foul and it was an early bath when west Yorkshire referee Martin Atkinson produced the second yellow.
Hartlepool played their part and will feel they deserved something from the game.
They went ahead in the 23rd minute with a superb strike by Hugh Robertson, when he netted with a curling left-foot free-kick from 30 yards after Michael Jackson had fouled Joel Porter.
Tranmere were level by the 27th minute via a penalty. Michael Nelson was judged to have brought down Eugene Dadi although he claimed he won the ball. Ryan Taylor then stepped up to send Jim Provett the wrong way from the spot.
Provett made an excellent early diving save at the feet of Dagnall and did well to hold a Dadi drive just after half time. The goalkeeper also held on well to a Jason McAteer effort in the 61st minute.
The winning goal came on 68 minutes. Dagnall found the corner with an angled shot from Dadi's pass. Provett got a touch but could not prevent the ball sneaking in.
It then became all hands to the pump for Tranmere in the closing stages when Kevin Betsy who was a 74th-minute substitute caused all sorts of problems.
Betsy saw one effort stopped by the outstretched leg of John Achterberg and then in the 89th minute he just failed to get a touch to a Porter cross in front of a gaping goal.
McAteer on his home debut did well enough for Tranmere before being replaced in the last minute by Danny Harrison.