Iceland had stunned Holland with a 2-0 win last time out and looked set to continue their good run of form when Ragnar Sigurdsson headed them into the lead after nine minutes.
But Pavel Kaderabek equalised in first-half stoppage-time and a mistake from goalkeeper Hannes Thor Halldorsson contributed to a Jon Dadi Bodvarsson own-goal which allowed the home side to open up a three-point lead at the top of the group.
The Czech Republic had the first chance as Ladislav Krejci’s cross was met by the head of David Lafata but the striker could only place his effort straight at Halldorsson.
Moments later, Iceland had the lead through Ragnar Sigurdsson.
Aron Gunnarsson’s long throw was flicked on by Kolbeinn Sigthorsson, who won the aerial battle with Petr Cech, but the ball looked to be drifting out of play. Birkir Bjarnason was having none of it, however, and headed the ball in from the byline for Ragnar Sigurdsson to plant home a simple header of his own from six yards after nine minutes.
Krejci had a chance to equalise soon after as he latched onto a lovely pass from Tomas Rosicky but dragged his shot across the face of goal when he would have been better squaring the ball across.
The Czechs were looking the more dangerous of the two sides and midway through the half Lafata had another chance as a long ball found him in the box but Halldorsson made a smart save with his feet.
In the 40th minute, Iceland had an opportunity to put themselves back ahead when Theodor Elmar Bjarnason fed Sigthorsson but Kaderabek made a smart challenge to block his shot wide.
Two minutes later it was the Czechs coming forward as Lafata headed Borek Dockal’s cross over the bar but they were ahead in first-half stoppage-time.
Krejci sent a free-kick into the box and when Daniel Pudil volleyed the ball into the box from the byline, Kaderabek was on hand to head home.
Lafata was proving a menace and volleyed wide after some juggling from Rosicky eight minutes after the break but it was an Icelandic blunder that would give the Czech Republic the lead just after the hour.
Jaroslav Plasil and Krejci combined well on the left and when the former cut the ball back from the byline, it hit Bodvarsson and dribbled to the near post where Halldorsson could not prevent it going in.
The home side were having by far the better of the second half but Iceland came close to an equaliser from another long-throw as Kari Arnason flicked a header towards Gylfi Sigurdsson and the Swansea midfielder rifled a volley from the edge of the box which hit the post.
Some smart play on the edge of the box then allowed Rosicky to set up substitute Vaclav Pilar but his curling shot went just over the bar as the final 10 minutes approached.
With six minutes remaining another long-throw caused chaos in the Czech box with Johann Berg Gudmundsson eventually bringing a smart save from Cech but the hosts held on.