There was drama in the 12th minute when United defender Iurie Iovu was sent off by referee Grant Irvine for a bodycheck on Cameron Russell.

However, the home side steadied and in the 31st minute Terrors captain Ross Graham headed in from a Will Ferry corner.

Attacker Amar Fatah added a second in the 55th minute before Spartans’ second-half substitute Mark Stowe reduced the deficit in the 78th minute with a deflected shot.

There were a few uncomfortable moments in the United ranks as the Scottish League Two side flooded forward before the final whistle confirmed a last-eight tie at fellow William Hill Premiership club Falkirk next month.

“Well, listen, we’re in the next round of the cup and that’s all that matters I suppose,” said boss Goodwin, who will consider an appeal of the red card.

“If you’d offered me a 2-1 victory, with 80 minutes on the clock and down to 10 men, then I’d have probably snapped the hand off you at that point.

“We knew tonight was going to be a difficult game. Spartans are a really good team, well-coached obviously, flying high at the top of their own division.

“It was never going to be straightforward, these games never are, but it’s made even harder obviously with the red-card incident.

“Credit to the players, they dug deep and managed to find a way to win the game.

“We’ve done what was expected of us tonight in terms of winning the game.

“And obviously, I think if we kept 11 men on the pitch, then of course, that might have made it a bit more straightforward than what it was.

“But there was certainly some nervy moments there going into the last five, 10 minutes of the game.

“But the boys have done what was required on the night. It’s certainly not a game that we’ll spend too long watching back.

“The most important thing in any cup competition is getting through and that’s what we’ve managed to do.”

Spartans boss Dougie Samuel was proud of his players after putting up such a valiant effort.

He said: “I thought the players were fantastic. I think that you come here hoping to do yourself justice and earn the respect of everybody that’s at the game.

“I always say that it’s about scoring a meaningful goal in these cup games and we certainly scored a meaningful goal because you could feel the atmosphere in the stadium change in an instant.

“It perhaps gave us a little bit more belief and obviously went a bit more positive from the get-go in the second half. I’m just hugely proud of the players.”