Kenny Miller put the home side ahead a minute from the break from a pass by skipper Darren Fletcher but that was levelled in the 78th minute by midfielder Jaroslav Plasil.
Fletcher restored Scotland's lead three minutes later after Miller returned the compliment but, in the 89th minute, substitute Danny Wilson conceded a penalty with a tackle on Jan Rezek and Michal Kadlec equalised from the spot to keep the visitors five points ahead of the Scots in second place.
Replays suggested Rezek had dived to win the kick, but referee Kevin Blom was not interested and, to make matters worse, Scotland were denied a late penalty of their own when Christophe Berra was booked for diving when it appeared he had been fouled in the Czech box.
The Scots were given a pre-match boost when Fletcher was selected to lead the side.
The Manchester United midfielder was back in the national side for the first time this year despite having only played two competitive games since the beginning of March after being hit by a lingering virus.
Berra was preferred to Wilson as partner to Gary Caldwell in the heart of Craig Levein's defence due to his greater experience.
But perhaps more importantly for the Scots' qualification hopes was the news that the visitors named an uncapped goalkeeper, Jan Lastuvka, in the absence of injured Chelsea number one Petr Cech.
The Tartan Army knew three points were needed - and also against Lithuania on Tuesday night - for their team to have a realistic chance of winning a play-off spot as runners-up to runaway Group I leaders Spain.
That considered, there was a predictable early surge from the home side, roared on by a capacity 52,000 crowd.
But in the fifth minute the Czechs broke and striker Milan Baros worked a one-two with Petr Jiracek only to balloon the return ball over the bar from 12 yards.
Then, with Hampden fervour dampened, Czech defender Jan Rajnoch headed a free-kick from captain Tomas Rosicky past the post from eight yards.
The visitors looked comfortable as they bossed possession as Scotland struggled to get at their defence and midfielder Scott Brown picked up a booking for a foul on Rosicky which meant he would miss the game against Lithuania.
It was not going to plan for Scotland and nerves began to jangle as the visitors, spearheaded by the impressive Baros, pushed forward with purpose.
At the other end Scotland's lone striker Miller was receiving little support from his midfield and Czech goalkeeper Lastuvka was having an easy debut.
The Czechs looked more likely to open the scoring as the game became stretched and increasingly frantic, but it all turned in the 44th minute when Miller took a pass from Fletcher inside the box and Lastuvka could only help the Cardiff striker's drive into the net.
The goal lifted the Hampden crowd at the break but Baros missed another good chance for the visitors a minute in to the second half when he slipped his shot past the far post.
Miller was then booked for a foul on Czech defender Tomas Hubschman which ruled him out of the visit of the Lithuanians.
But Scotland were playing with more confidence and for the first time in the game put the Czechs under some concerted pressure, although Allan McGregor had to make a save from Rosicky after the Arsenal player had made a yard of space for himself.
As some of the energy seemed to sap out of the Scottish legs, Czech Republic came back in to the game.
In the 65th minute, following another Rosicky free-kick into the box, the ball fell at the back post to defender Roman Hubnik who hit the side-netting, moments before Miller just failed to get on to the end of a James Morrison cross.
The visitors became increasingly dangerous and crosses flew in to the Scotland box.
But the Scots were struggling and in the 78th minute it was all square when midfielder Plasil forced in a cross from substitute Rezek, who had replaced Milan Petrzela.
However, in the 81st minute Scotland regained the lead when Miller skipped away from Rajnoch down the left and set up Fletcher who slipped the ball past Lastuvka from close range.
But, in the 89th minute, Wilson, on for Phil Bardsley, was adjudged to have fouled Rezek in the box and Kadlec slammed in the spot-kick.
Scotland were then denied a penalty claim of their own and Berra was booked for diving.