We hit back through Emmanuel Adebayor five minutes before half-time and levelled in the 58th minute when Gylfi Sigurdsson let fly from 20 yards.
But the full comeback didn't materialise as the visitors took a grip again and they missed the better chances as we finished the game with only nine men on the pitch with both William Gallas and Gareth Bale limping out of the action late on.
It's all set-up for the second leg at FC Basel's St Jakob Park next Thursday, April 11.
Andre Villas-Boas made three changes to the team that started at Swansea. Gallas was back in for Michael Dawson, Benoit Assou-Ekotto replaced suspended Kyle Walker while Lewis Holtby started on the left for Sigurdsson.
After a fairly low-key start, Basel burst into life with three chances in the space of a minute. Friedel made two fine saves to deny Fabian Schlar and Mohamed Salah before Salah blasted over from 16 yards.
Gareth Bale curled just wide from Holtby's incisive pass but then a blow as Aaron Lennon limped out of the action, Sigurdsson took over.
Naughton went close with a deflected drive from the edge of the box but the visitors then hit us with two goals in the space of four minutes.
Stocker started and finished the opener on the half-hour. There was a touch of fortune as he initially looked to pass but managed to bundle his way past two challenges and into the box before squaring for Marco Streller. The big forward turned and struck the foot of the post but the ball cannoned back to Stocker, who made no mistake from 10 yards.
It was soon 2-0 as Jan Vertonghen inadvertently flicked on Stocker's corner and Frei stooped to power home his header from 10 yards.
It could have been worse as Stocker soon broke through again, this time in the left channel and lifted his effort over the advancing Friedel but wide.
We needed a quick response and found it in the 40th minute. Bale's shot deflected to Adebayor, who missed his kick, Scott Parker kept the move alive and Adebayor was there to meet a tricky, high ball, volleying home shoulder-high past Yann Sommer.
Suddenly, the game changed and Parker was handed a golden chance to level just before the break. Sigurdsson weighted a pass through to Holtby, who was blocked six yards out but the ball ran to the midfielder, who appeared to want to make sure his effort didn't strike Holtby in front of him and side-footed wide.
The half-time whistle halted our momentum somewhat and both goalkeepers made saves at the start of the second half, Friedel a near-post block from Salah, Sommer at full-length to his left to claw away Naughton's piledriver.
Sigurdsson then raised the roof with the equaliser in the 58th minute. Cutting in from the right, the Iceland international feined to shot twice before finally letting fly and his shot appeared to clip Fabien Schar as it dipped under the crossbar.
We all hoped that would be the signal for the lads to go on and take the lead in the tie but Basel weren't finished yet.
Within two minutes of the equaliser, the lively Salah broke clean through on Friedel, only to sidefoot wide.
A combination of Vertonghen, Parker and Sigurdsson opened it up for Holtby to strike wide on 63 minutes and that was our last chance of note as Basel took advantage of the game stretching to catch us on the break.
Friedel touched over Stocker's free-kick, substitute Jacques Zoua missed the target from 10 yards and Salah shot tamely after good work from Markus Steinhofer.
To add to our difficulties on the night, Gallas and Bale both joined Lennon in limping out of the action.
Spurs (4-4-2): Friedel; Naughton, Gallas, Vertonghen, Assou-Ekotto (Dawson, 57); Lennon (Sigurdsson, 24), Dembele, Parker, Holtby (Dempsey, 63): Adebayor, Bale. Unused subs: Lloris, Caulker, Huddlestone, Livermore.
FC Basel (4-2-3-1): Sommer; Steinhofer, Dragovic, Schlar, Voser; Elneny, Serey Die (Cabral, 66); Salah (Degen, 83), F Frei, Stocker; Streller (Zoua, 72). Unused subs: Vailati, Ajeti, AFrei, Sauro.
Yellow cards: Spurs - Gallas, Parker. FC Basel - Frei.
Goals: Spurs - Adebayor (40), Sigurdsson (58), FC Basel - Stocker (30), Frei (34).
Referee: Mr M Mazic (Serbia).
The Swiss champions took a grip of the game in the first half with two goals in quick succession from Valentin Stocker and Fabian Frei.