Spurs went into the game with a narrow 2-1 lead from the first leg at White Hart Lane, with head coach Juande Ramos opting to partner Darren Bent and Fraizer Campbell in attack in Poland.
The opening minutes saw little in the way of goalmouth action, before Aaron Lennon started to look dangerous on the right wing for Spurs, but Wisla became the first side to threaten.
Just before the half-hour mark Pawel Brozek fired in a shot from just outside the area, but it was straight at Heurelho Gomes, who made a comfortable save.
Seven minutes before half-time Junior Diaz tried his luck with a 30-yard free-kick, but his left-foot drive flew straight into the gloves of the waiting Gomes.
Right on half-time, Spurs had Gomes to thank for a fine low save at his near post, after a one-two had allowed Radolsaw Sobolewski to run clear in the inside right channel.
Gomes then denied Junior Diaz right on half-time, as Spurs started to look shaky in defence.
Early in the second half Campbell finally found some space on the left, but saw his 25-yard drive deflected away for a corner.
Ten minutes after the break Luka Modric drifted inside off the left flank and his low, 20-yard right-foot shot forced a save from home keeper Mariusz Pawalek.
Two minutes before the hour Spurs made the breakthrough as Gareth Bale crossed from the left and Arkadiusz Glowacki headed into his own net under strong pressure from Campbell.
With 65 minutes on the clock Didier Zokora sprinted clear on the left side, but shot narrowly wide of the far post, with Campbell waiting for a pass in acres of space. Bent then rifled a shot inches wide of an upright as Spurs started to take a stranglehold on the game.
Ten minutes from time Bale rescued Spurs with a fine goal-line clearance following a corner from the right, as Ramos' side inched towards the group stages.
However, Wisla drew level on the day with seven minutes left to play, as Junior Diaz lofted the ball forward and Pawel Brozek ran on to loft the ball over the advancing Gomes and into the net.
The home side then piled on the pressure in the closing stages, but despite going close on several occasions, could not force the tie into extra-time.