The Merseysiders, who were 2-0 up by the 64th minute, should have won comfortably. But they conceded a goal on 71 minutes and only stayed in front because of a missed Hartlepool penalty six minutes later.
Tranmere's first goal came following the sending off when McCunnie brought down Ian Moore as he tried to retrieve the situation following a poor headed back-pass by Michael Nelson.
Chris Greenacre's spot-kick was saved by keeper Arran Lee-Barrett but the striker netted from the rebound.
It turned into a nightmare for Nelson when he turned a Chris Shuker cross into his own net in the 64th minute.
But then Hartlepool showed tremendous spirit. They pulled a goal back on 71 minutes when Richie Humphreys headed in at the far post from a cross by Willie Boland.
Six minutes later home defender Antony Kay floored Joel Porter to concede a penalty but substitute Tom Craddock blasted wide.
Tranmere settled it in stoppage time when Shane Sherriff headed in from a Paul McLaren free-kick, but the scoreline was tough on United who were unlucky to lose defender Sam Collins two minutes into the second half with a leg injury.
Sherriff took star-billing for Tranmere but their performance was very edgy and they failed to take several scoring chances.
Andy Monkhouse worked tirelessly for the visitors and was unlucky with a couple of good efforts. Porter also went close on a couple of occasions.
In the opening half Moore and Greenacre wasted gilt-edged chances for the home side.
After Tranmere went 3-1 ahead, they nearly grabbed a fourth but Lee-Barrett produced a fine diving save to deny substitute Calvin Zola.