Loading...
Bergvall struck with just four minutes left in north London, but Liverpool boss Arne Slot was furious that the Swede was still on the pitch to score his first goal for Tottenham.
Already on a yellow card, the 18-year-old had escaped a second booking moments earlier after tripping Kostas Tsimikas.
Tsimikas was out of position after the tackle when Bergvall scored from an attack that started on the left flank vacated by the Liverpool defender.
Tottenham's victory was a welcome tonic for Rodrigo Bentancur, who was taken to hospital after suffering a worrying injury.
Bentancur stooped to head a corner in the seventh minute and stayed on the ground after falling unchallenged.
His team-mates showed immediate concern and play was stopped as Bentancur received medical attention for nine minutes.
The 27-year-old was given oxygen through a mask during the treatment as a hush fell on the capacity crowd.
At half-time, Tottenham moved to ease fears over Uruguay star Bentancur, who only recently returned from a seven-game ban for using a racial slur about team-mate Son Heung-min.
"We can confirm Rodrigo is conscious, talking and will go to hospital for further checks," the club said in a statement on X during the half-time interval.
Responding to criticism of Tottenham's spluttering form and his attacking tactics, Tottenham boss Ange Postecoglou claimed earlier this term that he always wins a trophy in his second season.
The under-fire Australian could do with backing up that boast given Tottenham's poor form in the Premier League.
Tottenham last won a trophy when they lifted the League Cup in 2008 and the competition is shaping up as an opportunity to end that long silverware drought.
Liverpool won the League Cup last season in what proved to be Jurgen Klopp's last trophy.
Slot has taken Liverpool to the top of the Premier League and the Champions League since replacing Klopp, making this a rare flop from the Reds under the Dutchman.
It was Liverpool's first defeat in 24 games in all competitions since a 1-0 loss to Nottingham Forest in the league in September.
That was the only other loss endured by Slot this season and, following Sunday's disappointing 2-2 draw with lowly Manchester United, he is facing the first test of his prolonged honeymoon period on Merseyside.
The second leg at Anfield on February 6 will decide who advances to the final.
Newcastle won 2-0 at Arsenal in the first leg of the other semi-final on Tuesday.
Postecoglou had handed a debut to goalkeeper Antonin Kinsky, who replaced injured duo Guglielmo Vicario and Fraser Forster after signing from Slavia Prague in a £12 million ($14 million) deal at the weekend.
With Liverpool well below their best, the 21-year-old Czech wasn't forced into action until late in the first half when he held on to Alexis Mac Allister's header.
Slot grew frustrated with Liverpool's miscues, gesticulating at his backroom staff after Cody Gakpo's shot was saved by Kinsky.
There was more angst for Slot when keeper Alisson Becker turned an ambitious turn inside his own area, allowing Bergvall to steal possession and start an attack that ended with Pedro Porro chipping just wide.
Slot sent on Trent Alexander-Arnold and he almost made an instant impact with a shot that was cleared off the line by Radu Dragusin.
Darwin Nunez, another of Slot's substitutes, was denied by a fine save from Kinsky.
Bergvall escaped a red card before snatching his priceless winner in the 86th minute.
Dominic Solanke showed impressive strength and determination to hold off Ibrahima Konate, laying a pass into the path of Bergvall, who slammed low past Alisson.
Kinsky made a superb stop to repel Nunez's agile back-flick in stoppage-time as Postecoglou finally enjoyed a night to savour.