Former Uefa Cup winners Spurs marked their return to Europe with a deserved first-round, first-leg win.
Slavia lost their keeper Michal Vorel midway through the first half after he injured himself at a goal-kick.
But substitute Matus Kozacik was well beaten when Jermaine Jenas arrowed a shot into the corner of the net.
Having had little to do for the first hour Paul Robinson kept Spurs in front when he made a fine double save as Slavia searched for the equaliser.
Apart from that brief flurry of Slavia pressure the visitors - who won the Uefa Cup in 1972 and 1984 - always looked in control.
Didier Zokora provided plenty of drive from midfield, while Mido caused problems for Slavia when he drifted out to the left wing.
Early on Mido delivered a dangerous cross but Jermain Defoe was unable to reach the ball.
On 25 minutes Defoe swivelled quickly to create some space only to send his shot over the bar.
With Spurs so dominant in the opening stages Robinson had a quiet time, though he needed to be decisive in punching clear after Dusan Svento's dangerous run and cross.
Slavia had less luck with their goalkeeper Vorel and after his departure Kozacik was quickly into action, palming away Pascal Chimbonda's header.
But Kozacik was unable to keep out Jenas' shot as the Spurs midfielder struck a fierce effort past Slavia substitute keeper Kozacik.
Jenas' finish was exemplary, but so was the work of Zokora as he made a surging run before playing a precise pass to his midfield colleague in the build-up.
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The Ivory Coast international was quick to get Spurs back on the attack at the start of the second half.
Zokora broke clear after running almost half the length of the pitch before picking out Defoe, who headed the ball straight at Kozacik.
Midway through the second half Robinson was finally called into serious action when he pushed away Svento's free-kick and the Spurs keeper was up quickly to block Stanislav Vlcek's effort from the rebound.
But Slavia were unable to sustain their attacking momentum and Kozacik had to be alert to smother attempts from substitutes Edgar Davids and Robbie Keane.
Spurs last played in Europe seven years ago, but after this away win they look now well placed to reach the Uefa Cup group stages.
"It was the best result you could wish for, 1-0 away from home.
"It was a good goal - Jenas can do that, he can score goals and that is what you want in away games in Europe.
"To get a result is great."
Slavia Prague: Michal Vorel (Kozacik 28), Svec, Latka, Suchy, Hubacek, Janda (Necas 72), Jarolim, Hrdlicka, Svento, Vlcek, Gaucho (Fort 62).
Subs Not Used: Dosoudil, Gecov, Necid, Aracic.
Booked: Gaucho.
Tottenham: Robinson, Chimbonda, Dawson, King, Assou-Ekotto, Jenas, Huddlestone (Davids 71), Zokora, Tainio, Defoe (Keane 78), Mido.
Subs Not Used: Cerny, Lee, Stalteri, Ziegler, Davenport.
Booked: Assou-Ekotto.
Goals: Jenas 37.
Att: 14,869
Ref: Herve Piccirillo (France).