Luke Armstrong's first half dismissal for two extremely harsh yellow cards within three minutes made for a difficult evening at Prenton Park, with Tranmere running out 2-0 winners.
Lewis Warrington put the hosts ahead five minutes into the second half, before a Kane Hemmings penalty in the 65th minute ended all hopes of a comeback from the ten men of Town, despite a flurry of Harrogate chances after Tranmere's second.
Simon Weaver made two changes from the weekend's trip to Bristol as Alex Pattison and Lewis Richards replaced the injured Josh Falkingham and Brahima Diarra.
It was a scrappy start to the fixture, with passes often going astray and little goalmouth action. not helped by early head injuries to both Warren Burrell and Kane Hemmings causing a lengthly stoppage, though both were cleared to continue.
Armstrong was penalised for a foul on Peter Clarke in the 25th minute having closed down the Tranmere Captain and collided with the defender.
Two minutes later the same two went up for an aerial challenge, with Armstrong appearing to be dragged down by Clarke, only to get to his feet and be shown a second yellow card by Referee Darren Handley, much to the amazement of the Town players and staff.
The hosts forced Mark Oxley into a first save in the 33rd minute as the Town stopper kept out Elliott Nevitt's header that looked as though it could creep into the far corner.
Despite the numerical advantage, Town almost took the lead in the 39th minute as Mark Beck held up the ball and fed Jack Diamond, who shifted it onto his left before firing just wide.
Oxley was called into action again in the 42nd minute, keeping Josh Hawkes effort from finding the corner, before a Rory McArdle block deep into first half stoppage time ensured the tie remained goalless at the break.
Town could only keep their clean sheet for four minutes of the second half though as a neat Hemmings flick found Warrington, who carried the ball across the efge of the area before slotting into the corner.
Moments after Thomson had made a crucial goal line clearance, Tranmere were awarded a penalty in front of their vocal supporters after Muldoon had grabbed Clarke's shirt while defending a corner.
Hemmings calmly stroked the spot kick home to double his side's lead, though Diamond was inches away from reducing the deficit back to one just seconds after the restart.
Muldoon had prodded a pass through to Diamond, whose finish clipped Joe Murphy before being hooked off the line at the last second by Clarke.
It was the ten men of Town who continued to create the chances as the tie approached the last 20 minutes, Fallowfield seeing his attempt blocked by Calum Macdonald, before Diamond almost found got his name on the score sheet after a jinking solo run, but couldn't quite arrow the ball into the top corner from a narrow angle.
Town's last chance of scoring came when McArdle met Thomson's free kick at the back post and almost set up Calum Kavanagh for his first Town goal, though Murphy punched clear before the forward could provide the finishing touch and ensured his side ended the night with a clean sheet and three points.
Town: Oxley, Fallowfield, Burrell (Kavanagh 56), Thomson, Beck (Muldoon 57), Sheron, Pattison, Diamond, McArdle, Armstrong, Richards
Subs not used: Cracknell, Austerfield, Legge, Power
Booked: Armstrong, Thirlwell, Fallowfield
Sent off: Armstrong
Tranmere: Murphy, Dacres-Cogley, Macdonald, Davies, Hemmings (Foley 75), Hawkes, Warrington, Nevitt, McPake (Mcmanaman 75), O'Connor, Clarke
Subs not used: Doohan, Knight-Percival, Merrie, Jolley, Burton
Goals: Warrington 49, Hemmings 65 (p)
Booked: McPake, Clarke, Murphy
Referee: D Handley