Substitute Gylfi Sigurdsson made it 2-2 just before the hour when he cut inside and fired home a deflected shot to give Spurs a fighting chance in the second leg after the Swiss champions had stunned the home crowd by taking a two-goal lead after 34 minutes.
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Spurs' joy was tempered by Bale, their shining light this season, being injured in the closing stages after turning his ankle in a challenge with David Degen.
"I don't think there's any chance of him not being back for the [end of] season games. From what I understand from the medical department's first analysis everything is possible," manager Andre Villas-Boas told reporters.
The Portuguese said Bale may only be out for "the next two" games, which includes next Thursday's second leg.
Basel deservedly opened the scoring on the half hour thanks to Valentin Stocker.
The dangerous Mohamed Salah crossed from the right and captain Marco Streller turned sharply and hit the post, with Stocker on hand to put the rebound into the empty net.
Swiss league leaders Basel doubled their advantage four minutes later through Fabian Frei, who was left unmarked to head home after Spurs defender Jan Vertonghen could only divert a corner across the area.
Spurs striker Emmanuel Adebayor then stabbed the ball home ahead of the break to give the hosts hope and the Londoners should have gone in level but Scott Parker put the ball wide of an empty net from close range.
Iceland's Sigurdsson later managed parity to the relief of Villas-Boas.
"Today they created more than us. They had more chances. They were the best side tonight. They could have won the game," the manager said.
"The positive thing is we managed to get back into the tie. Had it finished 2-0 our task would have been very difficult in Basel."
Tottenham, who won the competition in its previous guise as the UEFA Cup in 1972 and 1984, were favourites to reach the semi-finals going into the tie but Basel have two away goals for the second leg at St Jakob Park.
"I'm probably annoyed not to have won tonight," Basel coach Murat Yakin said.
"We got off to a great start. It's a pity we couldn't go further but we were playing a top side. The draw was positive in terms of the second leg in Basel next week."
