The Reds actually fell behind inside 47 seconds, when Harry Kane headed in from close range.
But it was always going to be tough for Mauricio Pochettino's side to hold on for 90 minutes and they eventually conceded the equaliser shortly after half-time.
Jordan Henderson was the goalscorer and Liverpool completed their comeback in the 75th minute - and their second goal was a gift.
Spurs defender Serge Aurier clipped Sadio Mane's heels inside the box and referee Anthony Taylor had no choice but to point to the spot. Mohamed Salah made no mistake from 12 yards.
- Man Utd score 2000th PL goal
- Xhaka tells Arsenal fans to 'f*** off' after being subbed
- Check out our new GIVEMESPORT homepage
Of course, the defeat can't be pinned on just one player's mistake, but Aurier certainly didn't cover himself in glory on Sunday.
Post-match, Sky Sports pundit Roy Keane ripped into the Ivorian and his fellow full-back, Danny Rose.
In a scathing assessment, the former Manchester United midfielder described the Spurs pair as 'Dumb and Dumber'.
"Chalk and cheese," Keane said when asked to describe the difference between the two defenses.
"The two Tottenham full-backs were dreadful. Dumb and Dumber I call them. I thought they were really poor, you cannot compare them to the two Liverpool lads who were absolutely fantastic.
"The two full-backs today for Liverpool particularly going forward, okay there are parts of their game defensively they can improve but going forward absolutely fantastic
"And the two full-backs for Tottenham, I thought they were a joke, really abysmal."
That's pretty brutal analysis from Keane, but it's hardly surprising, given his reputation for pulling no punches.
At least he had something nice to say about Liverpool's full-backs!News Now - Sport News