The 18-year-old Swede rifled a superb finish into the Liverpool net in the 86th minute to reward the injury-hit hosts who shortly before had seen a Dominic Solanke goal ruled out.
Spurs were without 10 players for the tie and had lost 6-3 to Liverpool in the Premier League last month, but turned the form table on its head - albeit with a touch of fortune.
Match-winner Bergvall was lucky to avoid a second yellow card for a late tackle on Kostas Tsimikas moments before he fired home his winning goal to earn Tottenham and manager Ange Postecoglou a much-needed win.
Postecoglou rejected suggestions Bergvall had been lucky to be on the pitch when he scored.
"It's happened to us consistently, you look at our games, and we've asked the officials and they've said if you play advantage, as long as it's not a cynical tackle, then yellow card doesn't get (shown)," the Australian said.
"Now to me, that was pretty clear."
Postecoglou has faced external pressure after a nightmare run of form amid a horror injury crisis which deepened with Rodrigo Bentancur forced off early amid worrying scenes.
Bentancur was carried off on a stretcher in the 14th minute after falling to the ground at a corner.
Medical staff immediately ran onto the field as the Uruguay international lay face down on the turf, with players from both teams looking concerned.
Lucas Bergvall with the winner � pic.twitter.com/5R6y7DF5Px— Tottenham Hotspur (@SpursOfficial) January 8, 2025
Postecoglou confirmed later that it was his understanding that Bentancur was conscious.
"We took him to hospital just to get checked over. Worrying and always a concern but from what I know at this stage he'll hopefully be OK."
Liverpool beat Chelsea to win the League Cup for a 10th time last season but were nowhere near their best and could have few complaints as their 24-match unbeaten run in all competitions came to an end.
Arne Slot's side suffered only their second loss of the season but will still feel confident of turning around the tie in the second leg at Anfield next month.
Wednesday's match also included the time in English soccer a referee has made an NFL-style in-stadium announcement about the outcome of a video review.
Stuart Attwell used the public address system to announce that a goal by Solanke had been ruled out for offside.Â
Attwell communicated the decision via a wireless microphone to spectators inside Tottenham Hotspur Stadium and to TV viewers.
The League Cup semi-finals were chosen to pilot the process in England that has been widely used in other sports but Postecoglou was not impressed.
"I'm really surprised with how people in this country easily let the game change so quickly," he said.
"We need to be careful and why do we want to change the game so much? I just thought people will be more protective of the sanctity of the game.
"Especially in this country where you're custodians of the game, you have a song which says it's coming home, this is your game and it takes an Aussie from the other side of the world to ask about changes."
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