Henrik Larsson scored in stoppage time to ease Celtic's nerves in their Uefa Cup third-round first leg in Glasgow.
Larsson collected a through ball from Alan Thompson before stabbing home an early opener against Teplice.
Chris Sutton pounced on a defensive error to round the goalkeeper and roll home the second after just 12 minutes.
Thompson and Stephen Pearson squandered opportunities to increase the lead, but Larsson headed the third from a corner against a disappointing Czech side.
Celtic boss Martin O'Neill had made two changes, with Paul Lambert coming into midfield in place of the suspended Neil Lennon and Didier Agathe replacing John Kennedy in defence.
Teplice had lost five players through transfer since beating Feyenoord and Kaiserslautern in the previous rounds.
The visitors had played on the break against those two but paid the price after just two minutes for adopting an offside trap.
Larsson ran on to Thompson's through-ball before firing low through the legs of the exposed goalkeeper Tomas Postulka.
Teplice fell further behind in the 12th minute.
Vladimir Leitner failed to find Postulka with his back-header and Sutton nipped in to round the goalkeeper and score.
Thompson should have killed the tie off in the 17th minute after Larsson stepped over Pearson's cross after a clever move, but the midfielder fired over from eight yards.
Pearson had two great chances to strengthen Celtic's position when he beat the offside trap from Jackie McNamara's pass.
But Postulka saved his first effort and Tomas Hunal cleared his follow-up effort off the line.
Chris Sutton added the second goal at Celtic Park
Pearson also blasted over from the edge of the box after being sent clear by Sutton.
Teplice had been on the back-foot for much of the first-half but tightened up after the break.
A long-range effort from Thompson cleared the bar by a couple of feet as Celtic struggled to create chances.
Karel Rada wasted a rare opportunity to reduce the deficit after 81 minutes following a corner.
The Teplice defender fired wildly over after a nice turn 10 yards from the Celtic goal.
Stan Varga came close with two headers for Celtic before Larsson finally pounced on a Stilian Petrov corner.
Celtic: Douglas, Agathe, Balde, Varga, McNamara (Valgaeren 87),
Petrov, Lambert, Pearson (Sylla 72), Thompson, Larsson, Sutton.
Subs Not Used: Marshall, Hartson, Wallace, Beattie, Kennedy.
FK Teplice: Postulka, Dolezal, Rada, Hunal, Leitner, Ryska,
Verbir, Skala, Tesarik, Kowalik (Rilke 45), Masek.
Subs Not Used: Patrik Kolar, Sigmund, Kuchar, Horvath.
Booked: Skala, Rilke, Tesarik.
Referee: Konrad Plautz (Austria).