Spurs carried a 2-1 advantage into the second leg and the team news was dominated by the return of Paul Robinson in goal for the home side, with Radek Cerny paying the price for his error in Prague.
Juande Ramos' side soon extended their advantage, as Jamie O'Hara's left-foot shot from 20 yards took a deflection off a defender Martin Latka to leave Slavia keeper Michal Vorel totally wrong-footed.
Twenty minutes in Vorel beat out a 25-yard drive by Darren Bent, handed a rare start in place of Robbie Keane, before Aaron Lennon wasted the rebound by miskicking with the goal at his mercy.
O'Hara then flashed a dangerous ball across the area as Spurs began to dictate play. Bent was denied a goal 28 minutes in as his towering header was tipped onto the crossbar at full stretch by Vorel.
Ten minutes before the break Robinson was called into action, having to make a smart low save from Jaroslav Cerny's left-foot drive.
Five minutes after the restart Slavia were back on level terms on the night as Daniel Pudil swung in a superb far-post cross from the left flank and the unmarked Matej Krajcik buried the chance from close range.
That brought the first sign of nerves in the Spurs ranks, with both Latka and David Strihavka threatening with headers soon after.
Slavia were starting to dominate and midway through the second half an upright denied Strihavka, as his hooked, left-foot effort left Robinson stranded.
Fifteen minutes from time Robinson made a superb one-handed save to deny half-time substitute Milan Ivana, whose 25-yard free-kick was destined for the corner of the net.
Slavia continued to press in the closing minutes, but were unable to find a second goal which would have taken the tie into extra-time.