Wright’s deflected effort 10 minutes before half-time was cancelled out by Emmanuel Dieseruvwe’s 10th goal of the season against his former club.
But a fast start to the second half saw Halifax regain the lead through Senior’s close-range strike as the Shaymen put distance between themselves and Hartlepool in terms of the National League play-off places with help from an inspired performance from goalkeeper Sam Johnson.
Pools arrived at The Shay in need of a pick-me-up after the shock of Saturday’s defeat at Aldershot.
Having held a lead, Askey’s side contrived to lose it within 43-seconds – a result which saw them tumble down the table out of the National League’s top seven.
A perplexed Askey was able to receive a boost before the game with the arrival of defender Joe Mattock from Harrogate Town – the 33-year-old signing a one month loan deal with the club.
And Mattock went straight into the side in the heart of the Pools defence as Askey made two changes with Emmanuel Onariase being left out for the first time this season and Zak Johnson missing through injury after being forced off with a groin problem at Aldershot.
There was a return for Charlie Seaman at wing-back, which moved Luke Hendrie back into the centre of defence while the in-form Dieseruvwe returned to his old stomping ground looking to add to his nine goals already in a Hartlepool shirt since leaving West Yorkshire in the summer.
Pools arrived as close to the top three of the division as they did the bottom four but started well with Alex Lacey glancing Nicky Featherstone’s free kick wide before Joe Grey set the tone with an excellent driving run from halfway, skipping by two challenges onto his left before a wayward finish in the end.
Chris Millington’s side had won their previous three league games prior to this and woke up after 10 minutes when Florent Hoti’s low cross picked out Wright on the edge of the area and his volley was steered wide by the Hartlepool defence.
Pools were not out of the woods, however, as the resulting corner again found Wright, this time in the area, who was again unfortunate to see his effort deflect wide.
The following corner was half cleared out to the left where the ball was sent back into the area for Millenic Alli who brought an excellent save from Pete Jameson scrambling to his left.
Dieseruvwe forced Johnson into a save when peeling off to the right before Aaron Cosgrave tested Jameson after getting the better of Lacey on the angle of the area to curl towards the far corner.
The home side began to get on top of things as Alli was soon given a one-against-one with Hendrie – Alli heading onto his left before his strike at goal was deflected into the side netting.
Pools did get out midway through the half when Terrell Agyemang did well to win back possession on halfway as Hendrie then sent Seaman scampering away down the right, but the Doncaster Rovers man opted to cut back in onto his left where he was crowded out without being able to test Johnson.
It was Halifax who were in the ascendancy though with another series of corners, one of which almost crept by Jameson directly at his near post, before Wright gave the Shaymen the lead.
Wright was on hand to meet a low corner from the right towards the front of the area and his low strike deflected on its way to beating Jameson at his near post.
But Askey’s side weren’t behind for long.
After David Ferguson curled a free kick over the bar, Pools soon won a corner which would land in the six-yard box where Dieseruvwe reacted quicker than anybody to instinctively power beyond Johnson for his 10th goal of the season and drag Hartlepool level.
Alli wasted a free kick from a decent position on the stroke of half-time as the two sides went in level at the break.
But if Hartlepool felt they could reset and refocus at the break, Askey’s team talk was very quickly undone as the hosts flew out of the traps in the second half to retake the lead and almost take the game away from Pools.
Cosgrave first benefited from a fortunate ricochet off Tom Crawford to see his effort turned behind in what was the first of a number of corners before Senior broke what little resistance Hartlepool were offering.
Similar to Dieseruvwe’s equaliser, a corner dropped in and around the six-yard box where Senior was free to power into the bottom corner.
And having conceded twice within the space of 43-seconds at the weekend it was almost deja vu for Pools as Halifax raced forward from the restart with Cosgrave who brought Jameson into action again from distance with what needed saving low to his right.
Alli was next in line to try his luck when Wright’s cross swept its way to the back post with Jameson there to turn behind at his near post.
Alli then robbed Hendrie of possession deep in the Hartlepool half but Jameson did just enough in coming out to force the Halifax forward wide enough to fire off target.
Pools were on the ropes with, seemingly, no reprieve as Askey turned to his bench and Josh Umerah.
But after what had been something of an onslaught in the opening quarter of the second half, Pools were only denied an equaliser by a terrific save from Johnson.
Featherstone’s free kick was headed up into the air by Lacey which fell nicely for Dieseruvwe who reacted quickest again to get a snapshot at goal only for Johnson to push wide of the post.
Dieseruvwe then headed over from Grey’s cross as Pools finally appeared to have weathered the Halifax storm.
And they should have levelled midway through the half through Umerah.
Crawford did well to skip to the byline and beat his man and pull back to Umerah inside the six-yard box who rolled his man and had all of the goal to aim at only to power at the near post where Johnson saved with his feet.
Pools, to their credit, continued in search of an equaliser as Lacey then went close with a header at the back post from an excellent Matt Dolan cross.
Askey’s side still had time to force another top save from Johnson when Ferguson’s whipped cross was met by Umerah at the front post who this time did everything right but Johnson was in the right place at the right time to condemn Pools to yet another defeat.