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.
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."
"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."
