WREXHAM had the artistry of Wes Baynes to thank for their progress into the next round of the FA Cup, as he rifled home the decisive goal from 30-yards, some two minutes into added time.
Even then Maxwell had to save from Nicky Gray as the Shaymen almost grabbed the leveller they deserved for a fine defensive display.
Mike Williams in for Neil Taylor at left back was the only change to the side that has started the last two games.
Striker Gareth Taylor was in the wars early on, when he took a ball full in the face and needed a couple of minutes treatment from physio Ritson Lloyd before play could continue, he also needed several stitches to an eye wound at the final whistle.
Wrexham produced their first piece of decent football on 17 minutes and ended up with a left wing corner. The ball was played into the middle and a melee ensued with three Welshmen having a shot blocked before Mark Jones teed himself up from nine-yards - but fired wide.
Jones then broke from midfield a few minutes later, with the Halifax defence opening up in front of him, but his shot from the edge of the box lacked any threat.
Wrexham won a free kick on the side of the home penalty area after 22 minutes, when Curtis Obeng was fouled. Jones laid in a great cross that was met by Taylor six-yards out, but his flick header came back of the crossbar.
Christian Smith followed up with a long range effort that was deflected behind for a corner, with keeper Jonathan Hedge wrong footed.
McCluskey's flag was once again met by Taylor, but this time his header was just a bit too high and landed on the roof of the net.
Halifax attacked when they mustered numbers forward and won a corner on 37 minutes. Before the kick could be taken, Taylor was sent to the bench for treatment and when the ball came over it was flicked on for Steve Payne to send his header a foot over Chris Maxwell's crossbar.
Into time added on, Obeng was the victim of nasty foul by Scott Phelan, who was rightly booked. But the full back then extracted his revenge when play restarted and also had his name taken - which now means a one match ban for reaching five yellow cards.
Ht 0-0
After only eight minutes of the second half, there was a tactical switch as Silvio Spann returned from suspension to takeover from Mark Jones in midfield.
The Trinidadian made an immediate impact with a run and cross that was only just wide of the back post, with Hedge back peddling.
On the hour, it was Adrian Cieslewicz replacing McCluskey on the left wing.
A great one-two in midfield then set Andy Fleming away and his drag back picked out Cieslewicz, whose shot forced the first save of the game from either keeper.
Wrexham quickly lifted the tempo and Marc Williams got down the left to cross for Taylor, but he headed off target when well placed.
Marc Williams is having difficultly buying a goal at present and this was illustrated again on 70 minutes, when he was through on the keeper, but saw his first effort blocked and then with the ball running loose it was stabbed behind by a defender for a corner.
It was one-way traffic at this stage, but a combination of Halifax's massed ranks in defence and some poor approach play by the visitors hardly helped Wrexham's cause.
The Reds had to be careful though, as a Shaymen breakaway saw substitute Paul Harrison fire over from the edge of the box.
A Halifax corner shortly afterwards was spilled by Maxwell, but Payne missed for the second time on the afternoon, firing well high as the ball dropped at his feet six-yards high.
Then came the late, late drama of Wes Baynes' spectacular 30-yard goal, which went in off the underside of the crossbar and Chris Maxwell's save to deny an equaliser.
On possession alone the Dragons were well worth their win, but in reality they never turned that advantage into scoring chances and it was tough luck on the home side, who did deserve a second chance at the Racecourse.
Halifax: Jonathan Hedge, Aaron Hardy, Dan Codman, Steve Payne, Ryan Crossley, James Riley, Nick Gray, Scott Phelan, James Dean, Tom Baker, Richard Marshall (Paul Harrison 80).
Subs: Phil Senior, Mark Hotte, Tom Penford.
Wrexham: Chris Maxwell, Curtis Obeng, Mansour Assoumani, Frank Sinclair, Mike Williams, Jamie McCluskey (Adrian Cieslewicz 60), Mark Jones (Silvio Spann 53), Christian Smith, Andy Fleming, Marc Williams (Wes Baynes 80), Gareth Taylor.
Subs: Neil Taylor, Ashley Westwood, Hedi Taboubi, Lamine Sakho.
Referee: J Simpson (Lancs)
Attendance: 2,843
Away: 400ish
Bookings -
Halifax: Riley (42, foul), Baker (44, dissent), Phelan (45, foul)
Wrexham: Obeng (45, foul), Baynes (90, ungentlemanly conduct)
