Teenager Ryan Taylor earned Tranmere a place in the second round of the Worthington Cup, with a brilliant late goal.
It came eight minutes from the end, just four minutes after Hartlepool had equalized to set up a frantic finish to a scrappy game.
Both sides had chances to take an early lead, the best falling to home striker Eifion Williams in the second minute. But after being sent clear by Richie Humphreys, he delayed his shot and keeper John Achterberg made a great one-handed save.
But Rovers opened the scoring after 36 minutes, when striker Simon Haworth bundled the ball over the line after a left-wing corner from debutant Taylor.
The Merseysiders looked in control of the game, but 12 minutes from time United shook them with an equalizer. Adam Boyd forced defender Gareth Roberts into slicing his clearance across the penalty area and Williams was on hand to guide a left-foot shot home from ten yards.
But the home sides' joy didn't last long, as Taylor sealed Rovers victory by curling a 25-yard free-kick into the top corner.
The game ended in controversy as Pool had two late penalty appeals turned down, one for handball and the other the a trip on Darrell Clarke.
Tranmere manager Ray Mathias said: "I was very pleased for Ryan to score the winner like that.
"He enjoyed his goal, and we deserved the win. It was a difficult game, but we handled it well."
Hartlepool boss Chris Turner said: "A couple of decisions went against us and I'm disappointed we've gone out of the competition. But promotion is our top priority and that's what we have to continue to aim for."
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