Manchester United's Brazilian midfielder Antony (L) vies with Tottenham Hotspur's English defender Djed Spence during the English League Cup quarter-final. [AFP]

Tottenham survived two calamitous errors from stand-in goalkeeper Fraser Forster on Thursday to beat Manchester United 4-3 and set up a League Cup semi-final against Liverpool, staying on track for their first trophy since 2008.

The home side were cruising at 3-0 in the 54th minute of a captivating tie in London after two goals from Dominic Solanke and one from Dejan Kulusevski.

But Forster's mistakes allowed substitutes Joshua Zirkzee and Amad Diallo to pull the score back to 3-2 with 20 minutes to go.

It was one-way traffic after that, with United totally on top, but Spurs scored a fourth as Son Heung-min found the net from a corner and they held on despite a late Jonny Evans goal.

Tottenham will face Premier League leaders Liverpool in the two-legged semi-finals, with Arsenal taking on Newcastle.

Spurs boss Ange Postecoglou said his injury-hit team inflicted pain on themselves but gave a passionate defence of his gung-ho approach.

"It should have been a lot more comfortable there, but having said that, I still can't get away from the fact that this group of players have done an unbelievable job at the moment to get us through this," he said.

The Australian added: "I know people will say, "Well, don't take any risks' and all that sort of stuff, but we wouldn't be scoring four goals and five goals.

"It's the hardest thing in the game to do, score goals, and we're doing it with bare bones."

Tottenham, 10th in the Premier League, have not won silverware for 16 years, when they lifted the League Cup under Juande Ramos.

But they are now just one stage away from a Wembley final in March, with Postecoglou still on track to deliver on his bold statement that he always wins a trophy in his second season at a club.

New United boss Ruben Amorim is back down to earth with a bump after his side's dramatic 2-1 Premier League win at Manchester City on Sunday.

Amorim made five changes from the team that beat City while Spurs had six academy players on their bench.

Marcus Rashford was left out of United's squad for the second consecutive game but Alejandro Garnacho, also absent on Sunday, was on the bench and came on as a second-half substitute.

- Solanke double -

Tottenham opened the scoring in the 15th minute when Solanke reacted quickest after United goalkeeper Altay Bayindir, in for Andre Onana, parried a shot from distance into his path.

Kulusevski doubled Tottenham's lead moments after the restart, finishing unerringly when Lisandro Martinez failed to deal with a James Maddison cut-back, only succeeding in diverting the ball into the Sweden international's path.

Spurs were 3-0 up when Solanke ran onto a long ball over the top, drifting inside Martinez and Evans and finishing with confidence.

But control turned to chaos just after the hour mark following some incredible goalkeeping errors from Forster, deputising for the injured Guglielmo Vicario.

Forster, being closed down by Zirkzee, passed straight to Bruno Fernandes, whose ball found Zirkzee and the Dutchman slotted the ball into an empty net in the 63rd minute.

Minutes later United scored again when Forster dithered after receiving a back pass.

Diallo closed him down in a flash and slid in as Forster tried to clear, with the ball hitting Diallo and ending up in the net.

United had further chances but instead Son gave Tottenham a cushion in the 88th minute.

Even then United had time to find another, with Evans heading in from a corner, but they ran out of time.

"We were not the best team in all of the game, but most of the parts I think we were the best team," said Amorim.

"I think we disconnected for eight minutes. It was really hard to recover from that, but then the lads did a great job."