Boyd's two goals took his tally for the season to 29 and gave his hometown team a chance to play in a final at last, after failing in their previous four semis.
Pools had to survive a lot of pressure from Tranmere in the second half of a thriller of a game, but they produced one of their best performances of the season and were full value for their victory.
Hartlepool were clearly the better team in an entertaining first half and deserved their interval lead.
The goal came after 32 minutes when Jon Daly headed down a long throw from the right by Richie Humphreys and Boyd turned well in front of goal to slam the ball in from close range.
Daly missed a clear chance to make it 2-0 just two minutes later when he lifted his 15-yard shot high over an open goal after Boyd's great work on the left.
In first-half injury-time Tranmere's Mark Rankine had a close-range goal disallowed for offside.
Rovers looked a better side after the break and defender Ian Goodison wasn't far off target with a glancing header from their first corner of the game, on 50 minutes.
But Hartlepool doubled their lead in the 68th minute as Boyd scored his second.
He picked up a flicked pass from substitute Joel Porter and ran across the face of the Tranmere area before hammering a low left-foot shot into the net from 20 yards.
Matty Robson almost made it three on 77 minutes when his curling free-kick was tipped round the post by John Achterberg, but in the dying seconds Robson had to be smart to clear a shot from Eugene Dadi off his own line after a scramble deep in the Pools area.