Spurs were forced to field Didier Zokora at centre-half, with Teemu Tainio filling in at right-back, while goalkeeper Radek Cerny started against his former club.
Juande Ramos' side made the perfect start as just four minutes in Jermaine Jenas was tackled on the edge of the area and when the ball broke loose, Dimitar Berbatov rifled home a superb, low right-foot half-volley.
The goal settled Spurs down nicely and they continued to dominate the play as Slavia failed to pose any sort of threat.
After 26 minutes Aaron Lennon almost doubled the lead, but his low drive was blocked well at his near post by home keeper Martin Vaniak.
On the half-hour mark it was 2-0 as Jenas released Robbie Keane and he tucked his finish past the advancing Vaniak from the left side of the area.
Vaniak was the star of the show just before the break, as he made a superb double save from Berbatov and then pushed away a stinging 25-yard drive by Tom Huddlestone.
Huddlestone clipped the outside of the woodwork early in the second half, before Slavia finally threatened as Frantisek Drizdal headed over from Jaroslav Cerny's free-kick.
Spurs seemed to be cruising to a comfortable victory, but 21 minutes from time Cerny fumbled a deep cross to the back post from the left and allowed David Strihavka to bundle the ball home from close range.
Berbatov came close to restoring the two-goal cushion as he forced Vaniak into another outstanding save, tipping away a dipping 20-yard free-kick.
However, Slavia piled on the pressure late on, with Strihavka firing wide when well placed and Erich Brabec heading against the crossbar from Cerny's inswinging corner from the right.
Spurs held on though and are in pole position to make it through to the last 16 of the competition.