Ritchie Humphreys struck the decisive spot-kick after Ryan Taylor and Ian Sharps had missed for the home side.
Tranmere went into the game 2-0 down but Taylor's 70th-minute free-kick pulled one goal back before David Beresford's sweet drive levelled it.
A goalless extra-time led to penalties and Hartlepool held their nerve to win.
Tranmere boss Brian Little:
"I could not have asked for more. We did everything we could have done.
"Everybody played well, worked hard and I thought we played some outstanding stuff at times.
"I thought we were the better team by far but all credit to Hartlepool. They hung on and I wish them well because they are a decent set of lads."
Tranmere: Achterberg, Taylor, Jackson, Sharps, Goodison (Beresford 55), Hall, Rankine, McAteer (Harrison 20), Roberts, Hume, Dadi (Dagnall 119).
Subs Not Used: Whitmore, Linwood.
Booked: Hume, Achterberg.
Goals: Taylor 70, Beresford 87.
Hartlepool: Konstantopoulos, Barron (Tinkler 66), Nelson, Westwood, Robson, Williams, Humphreys, Strachan, Sweeney, Boyd (Butler 85), Daly (Porter 72).
Subs Not Used: Provett, Clark.
Agg (2-2): Hartlepool win 6-5 on penalties.
Ref: M Atkinson (W Yorkshire).