Adam Boyd netted a brace for the home side with his first coming from a smart finish after he controlled Jon Daly's knockdown and instantly slotted home.
Daly missed a gilt-edged chance when he blazed over but striker Boyd spared his blushes with a 20-yard strike.
Tranmere boss Brian Little:
"It's going to be hard work for us now. The second goal has given them a huge boost.
"They scored goals at periods when we looked comfortable and I was disappointed with both goals.
"At home we will have a go and give them a game."
Hartlepool: Konstantopoulos, Barron, Nelson, Westwood, Robson, Williams, Sweeney, Strachan, Humphreys, Daly (Porter 63), Boyd (Tinkler 90).
Subs Not Used: Provett, Clark, Butler.
Goals: Boyd 32, 68.
Tranmere: Achterberg, Jackson, Sharps, Goodison, Taylor, McAteer, Whitmore (Dadi 79), Rankine, Roberts, Hall (Beresford 83), Hume.
Subs Not Used: Howarth, Linwood, Harrison.
Booked: Hume, Jackson.
Ref: B Curson (Leicestershire).