Valentin Stocker and Fabian Frei stunned White Hart Lane before the break but Emmanuel Adebayor and Gylfi Sigurdsson gave Spurs hope of progressing in the second leg in Switzerland.
Basel started the brighter and went close three times within the first 10 minutes as Brad Friedel saved from Fabian Schar and Marco Streller before Markus Steinhofer volleyed over.
Aaron Lennon then went off injured to be replaced by Sigurdsson as Spurs struggled for rhythm and things got even worse when the Swiss side took the lead on the half-hour mark.
Streller produced a neat turn before seeing his shot bounce back off the post and there was Stocker to calmly slot home the rebound.
Worse followed for the home side when Jan Vertonghen inadvertently flicked on a corner at the near post and Frei pulled away to head the ball past Friedel.
Basel could have added a third goal when Stocker chipped Friedel only to see his effort drift wide of the post, but Adebayor pulled one back to raise spirits five minutes before the interval.
The striker's first effort hit his standing foot but Scott Parker did well to recycle play and the Togo international was on hand to force ball past Yann Sommer.
Spurs could even have gone in level when Lewis Holtby bundled his way through on goal but Parker's measured finish clipped the prone German and deflected wide with the goal gaping.
They didn't have to wait too long to be on level terms, however, as Sigurdsson's deflected effort from distance beat Sommer before the hour mark.
If that was supposed to see Spurs kick on for victory, Basel had other ideas with Mohamed Salah immediately missing the second of two good chances as the visitors continued to press.
But the scoreline stayed at 2-2 and a late injury to Gareth Bale added to the feeling that Andre Villas-Boas' side have it all to do when they travel to Switzerland for the away leg next Thursday.