Zac Sapsford's stoppage-time penalty sealed an unlikely comeback victory for Dundee United to deny Livingston a first Scottish Premiership win since August and edge their apparently inevitable relegation even closer.

Lewis Smith's second-half double looked to have given the visitors a real chance of a first triumph since the summer, cancelling out Will Ferry's opener.

But Krisztias Keresztes headed in a 75th-minute equaliser for haphazard United before Sapsford's penalty won it with the last kick of the game.

The win keeps United in seventh, and all-but removes them from the relegation equation, but Livingston are now 12 adrift of Kilmarnock with 15 points to play for.

United boss Jim Goodwin had made four changes from the team that lost at Ibrox last week, and they continued their decent form of late, taking a 19th-minute lead.

Max Watters played the ball out to Ferry in acres of space on the left. He carried the ball into the box, shifted on to his right foot and rifled a low shot past Jerome Prior.

Livingston remained well-organised and weren't lacking effort but United looked on top until the end of the half, when Livingston served notice of the threat they could carry from set pieces.

Soon after the restart, Marvin Bartley's side got their reward. Joel Nouble robbed Iurie Iovu out wide, and cut the ball back for Smith to hit a high finish into the net.

Moments later, Smith struck again. Goalkeeper Prior spotted an opportunity and hit a long ball down the middle, leaving Smith one on one with Ross Graham. The winger unleashed a powerful low shot that left Richards without a chance.

With no league wins since August, Livingston perhaps understandably tried to defend their lead. But United found an equaliser when Keresztes rose highest to bullet in Ferry's corner.

The drama wasn't over though, and in the final minute, Brooklyn Kabongolo fouled Sapsford to concede a penalty and give United a late chance to win it.

The Australian forward stepped up and made no mistake to leave Livingston with what looks like an impossible job to avoid a return to the Championship.

United's season has been pockmarked by inconsistency, so Jim Goodwin will have been delighted to see them win a third Premiership home game in a row for the first time since October 2021.

Result aside, the game seemed to underline United's failings. After Ferry's opener, there was plenty possession but a lack of chances. They nearly paid the price.

Goodwin spoke beforehand about his frustration at goals conceded and he would have been furious to see Iovu dispossessed so easily and Smith left alone in the middle of the area for the opener. The second goal wasn't much better.

On the plus side, even though there was a lack of invention, there was no shortage of effort.

For Livingston, this felt like a last faint chance of survival falling away. A handful of draws had kept them in touch but a win was needed with time running out.

Despite having tasted victory just once in their last 32 games, there was an energy and belief when they drew level and taking the lead gave an opportunity to build momentum going into a run of games against sides in the bottom half.

Instead, conceding from a set piece and then a mistake leaves the club staring at the inevitable. These final five games will be their last in the Premiership for a while.

Dundee United manager Jim Goodwin told BBC Scotland: "I think we probably stole the points in the end.

"First half , we were relatively comfortable and Livingston didn't really carry any threat. We were on top in the game and had one or two half-chances and Will Ferry scores a really good goal.

"I was relaxed and didn't see the start to the second half coming. Two really poor goals from our point of view.

"We gave ourselves a mountain to climb. Credit to the players, I suppose, they showed character in the dying moments to get the equaliser and then a rash tackle allows Zac Sapsford to win it with the last kick of the ball.

"The character is the main thing I'm pleased with but I'm really frustrated with the goals we've conceded. It's happened far too many times this season. I sound like a broken record because I seem to talk about it every week.

"We know that's a weakness and an area we need to strengthen in the summer. But going forwards we carry an attacking threat.

"It wasn't pretty but five goals entertains the fans, it's three points and we remain in seventh."

Livingston manager Marvin Bartley told the club's social media account:

"It's a really tough one, especially with the manner of the goals we conceded today. It's difficult to take.

"I don't think Dundee United had to do too much today to score other than be a little bit stronger and a little bit more aggressive to get to the ball.

"Some stern words were said at half time and some tactical changes and I was happy with their reaction but if you concede three goals away from home it's almost impossible to get anything out of games.

"I felt the boys gave an awful lot today. They're hurting and the staff are as well, it's a hard one to take."

Both sides have a break before the split as the Scottish Cup semi-finals take centre stage next weekend.

United begin their post-split fixtures with the Dundee derby at Tannadice on Sunday, 26 April (14:00 BST). Livingston play a day earlier, travelling to St Mirren (15:00).