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The Tayside outfit led 1-0 through Steven Fletcher when defender Ryan Edwards was sent off for a 28th-minute challenge on the Hearts midfielder Andy Halliday. Unable to initially exploit their numerical advantage, the hosts toiled and needed manager Robbie Neilson’s intervention with some pivotal substitutions to turn this game in their favour.

He introduced forward Stephen Humphrys at half-time before midfielder Jorge Grant, defender Alex Cochrane and striker Garang Kuol took the field. All four played their part in the late transformation as Lawrence Shankland’s 71st-minute equaliser preceded Cochrane’s goal five minutes later. Humphrys then stole the show with an outrageous third from inside his own half.

Neilson was widely criticised after Wednesday’s 3-0 defeat by Rangers but earned a good deal of redemption with his decisions inside a tense Tynecastle Park. A late red card for Josh Ginnelly came just seconds before Humphrys unleashed his goal of the season contender.

United contributed much to a compelling encounter but they are now almost nine years without a win at Tynecastle, and seven without beating Hearts anywhere. Today was Big Hearts Day at Tynecastle as the Edinburgh club raised funds for their official charity wing. They got no gifts from the opposition, it must be said.

Dundee United lost the creative Jamie McGrath when he suffered an injury during the pre-match warm-up and was replaced in the starting line-up by Peter Pawlett. He was to put in a fine 50-minute display until he also succumbed to injury. Hearts reverted to a more orthodox midfield set-up after Wednesday’s experiment against Rangers as Andy Halliday returned to add both steel and craft.

Having drawn at Livingston and lost to Rangers in their last two matches, this was a fixture the hosts dearly wanted to win to regain some momentum. Chilly and damp air around Gorgie suggested energy and dynamism would be the order of the day.

The travelling support didn’t take long to declare who they blame for Dundee United’s current fight against Premiership relegation. Chants of “Asghar, Asghar, get to F***” roared from the Roseburn Stand on eight minutes aimed at the Tannadice Park sporting director. Less than 60 seconds later, those same fans were celebrating the opening goal of the afternoon.

Hearts Stephen Humphrys celebrates his stunning goal to make it 3-1 against Dundee United.

Craig Sibbald’s pass released Ilmari Niskanen down United’s left, his low delivery was initially stopped by Kye Rowles’ sliding challenge. Fletcher stayed on his feet to slide the loose ball under the advancing Hearts goalkeeper Zander Clark from close range.

That agitated the locals and Glenn Middleton soon rasped a shot into Clark’s chest as the visitors probed for a second goal. They were moving the ball around notably better than their hosts. When out of possession, manager Liam Fox had clearly ordered those in tangerine to filter back into a 5-4-1 formation without any gaps. Consequently, Hearts found it difficult to break the opposition down during the opening period.

The dismissal on 28 minutes should have worked in their favour immediately but didn’t. Edwards lunged into a midfield challenge with Halliday and appeared to play the ball before following through on the Hearts player. Referee Nick Walsh checked a pitchside monitor on VAR’s advice before issuing Edwards a straight red card for serious foul play. United’s 5-4-1 now became a permanent 4-4-1 as they faced up to a numerical disadvantage whilst 1-0 ahead.

Fletcher and Middleton could easily have scored a second before half-time. A long kickout from the United goalkeeper Mark Birighitti was allowed to drop in behind the Hearts defence for Fletcher to bring down, but he dispatched a hurried left-footed attempt high over the crossbar despite having time to do better.

Then came a moment of controversy when Middleton rattled Clark’s left post. His effort came after Fletcher’s shot struck Rowles and rebounded into his path. Despite claims the the ball hit the Australian’s arm, play continued with no indication of a VAR check.

A similar moment occurred early in the second half when Barrie McKay’s low delivery into the penalty box appeared to bounce up and strike the United defender Charlie Mulgrew on the arm. Again, the game carried on. Hearts were more assertive in their play but were being made to work relentlessly to prise open the well-marshalled visiting rearguard.

United camped in their own half and defended in numbers. Their resolve remained until the 71st minute. A sublime Hearts passing move saw the ball worked out to the left flank, where another McKay cross spun up off Liam Smith. Shankland, 12 yards out, took it down for a left-footed shot on the turn which deflected off the unfortunate Scott McMann and into the bottom corner.

Five minutes later, Hearts struck again after a move just as aesthetically pleasing as the equaliser. Substitutes Grant, Kuol and Humphrys helped move the ball from right-back to left-wing. McKay then slipped a pass to another replacement, Cochrane, who produced a touch and finish the envy of any centre-forward to put his side 2-1 ahead.

Humphrys might have made the victory safe with a late drive which rebounded off Birighitti’s right post before seven minutes of stoppage time. A red card for Ginnelly came after two yellows seconds apart – one for time-wasting and the other for sarcastically applauding the first. The game’s best moment was still to arrive, though.

In the dying seconds, Humphrys held off Arnaud Djoum’s midfield challenge to send an almighty screamer from his own half high over Birighitti into the net with his supposedly weaker left foot. The trajectory of the ball merely mirrored the on-loan Wigan forward’s soaring popularity in Gorgie as he rounded off the afternoon.

Hearts (3-4-2-1): Clark; Hill (Kuol 69), Sibbick, Rowles (Cochrane 69); Forrest (Humphrys 46), Halliday (Grant 61), Snodgrass, Kingsley (Neilson 88); Shankland, McKay; Ginnelly.

Dundee Utd (3-4-2-1): Birighitti; Edwards, Mulgrew, McMann; Smith, Sibbald (Freeman 74), Levitt, Niskanen (McLeod 83); Pawlett (Djoum 51), Middleton; Fletcher.

Referee: Nick Walsh.

Attendance: 18,279.

Hearts 3-1 Dundee Utd: Robbie Neilson's decisions change the game, a Stephen Humphrys screamer plus two red cards