The Blues fell behind to Christian Eriksen's excellent early strike but goals from Pedro and Victor Moses ensured that Spurs' wretched run at Stamford Bridge continues.
The reigning champions will fancy their chances of progressing to the semi-finals after picking up an away win against the Basque side in Thursday's first-leg clash.
The visitors came from behind to earn a remarkable victory at Camp Nou, in a result that simultaneously dents the hosts' title hopes and boosts those of Atletico Madrid.
The Nerazzurri took the lead through Ivan Perisic but were unable to hold onto their lead in a game that ended in a stalemate – a result that benefits neither team.
Taison and Olexandr Kucher put the hosts in a strong position midway through the first half and, despite a fightback from the Belgians, Eduardo netted late to maintain an advantage.
Luis Suarez put the Blaugrana in front but they were denied a precious victory late on as Zinedine Zidane's men maintained their six-point lead over their rivals in La Liga.
The side coached by Jorge Sampaoli prevailed on penalties when the nations clashed in the 2015 decider, but Gerardo Martino's men will be keen for revenge in the US.
The Belgian has no doubt the trio are top of the pile after witnessing their feats on a daily basis, while he is content with his bit-part role under Luis Enrique at Barcelona.