Livermore's new deal, until 2011, had been announced earlier in the day and he found the net shortly after coming on as a substitute in the 80th minute, cancelling out Bojan Krkic's opener.
Spurs boss Harry Redknapp auditioned four possibilities to plug the hole in the centre of his defence during the clash. With Spurs short on numbers, Vedran Corluka, Tom Huddlestone, Pascal Chimbonda and youngster Dorian Dervite filled in at centre-back but could not prevent Bojan getting on the scoresheet.
The Spanish and European title holders selected a severely weakened team, with only Yaya Toure remaining from the side that defeated Manchester United two months ago in the Champions League final.
Eric Abidal, who was suspended for that clash, started and so did Bojan but Spurs' makeshift defence were spared an evening trying to keep out Thierry Henry, Lionel Messi or Zlatan Ibrahimovic, who has agreed personal terms ahead of a move from Inter Milan.
With Jonathan Woodgate, Michael Dawson and Ledley King sidelined, Huddlestone had to drop back from midfield to centre-back, with Corluka shifting inside from the right from the start.
Redknapp went with Jermain Defoe in attack on his own and Spurs struggled to make chances, allowing Barcelona to settle into the game.
They took the lead in the 32nd minute when Toure went on a mazy run past Wilson Palacios and Corluka. Huddlestone tackled him cleanly but the ball ran for Bojan, who lashed home at the near post.
It could have got worse when former Chelsea forward Eidur Gudjohnsen chipped through for Pedro Rodriguez to tuck home, but he was harshly ruled offside.
Luka Modric struck the bar for Spurs in their first genuine attack, with Benoit Assou-Ekotto getting an effort tipped over when the rebound eventually fell for him.
Barca changed their entire side at the break, while Robbie Keane was among the four substitutes Redknapp brought on.
It meant Spurs were 4-4-2 and they had a huge penalty appeal turned down just before the hour mark when Albert Dalmau appeared to handle when he controlled a corner aimed at the far post.
Heurelho Gomes saved well when Jeffren Suarez was sent through, while Modric had a close-range effort bravely blocked by substitute goalkeeper Jose Maria Pinto.
Livermore headed home in the 83rd minute, getting on the end of Assou-Ekotto's cross.