Czech Republic forward Patrik Schick scored a second-half equaliser to deny Georgia their first major tournament win at Euro 2024.
Georgia and Czech Republic both came into the contest with hopes of claiming all three points after losing their opening games to Turkey and Portugal respectively.
Giorgi Mamardashvili was required to make numerous stops to keep his side on level terms following a fast start from a determined Czech Republic side.
However, Georgia's defences were eventually breached in the 23rd minute, only for Adam Hlozek's goal to be chalked off for handball.
Czech Republic were left cursing their luck when a handball infringement at the opposite end of the pitch gave Georges Mikautadze the opportunity to fire home a penalty in first-half stoppage time.
Georgia's precarious lead lasted until the 59th minute when Patrick Schick followed in on Ondrej Lingr's header to net his sixth goal in seven European Championship appearances.
Saba Lobjanidze spurned a a golden opportunity to snatch all three points in stoppage time, but the Georgia forward failed to keep his composure and blazed his wayward shot over the bar.
The two nations now have a point apiece and are two points adrift of the top two ahead of the meeting between Turkey and Portugal in Group F's other game on matchday two.
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Mikautadze keeps his compsoure
Mamardashvili was swiftly forced into action, pulling off a superb double save to demonstrate why he was one of the standout goalkeepers in La Liga last season.
The Valencia shot-stopper stuck out a big left boot to thwart Hlozek, before quickly gathering himself to push Schick's shot away from danger.
Mamardashvili had no time to admire his work as he was soon required again to make a diving stop from Schick's headed effort.
Ivan Hasek's side thought their persistence had finally paid off in the 23rd minute when a dangerous long throw found Hlozek, who bundled the ball home after seeing his initial effort saved.
However, replays showed the ball struck Hlozek's arm before rolling into the net, leaving the officials with no choice but to chalk it off for a handball infringement.
After being second-best for the majority of the first period, Georgia began to grow into the contest as the half wore on, before they eventually created their first meaningful chance in stoppage time.
Khvicha Kvaratskhelia's dangerous free kick found its way to defender Guram Kashia, who produced an exquisite first chance to create the space to unleash a left-foot shot, only to see his effort smartly saved by Jinrich Stanek.
Just as Kashia was reflecting on his miss, the VAR officials and referee ruled that Robin Hranac had handled Kvaratskhelia's delivery, giving Georgia the chance to go to the penalty spot.
Mikautadze put the weight of a nation on his shoulders to send Stanek the wrong way and guide his penalty to the opposite side of the goal.
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Schick pulls Czech Republic level
After taking a slender lead into the break, Georgia threatened to double their advantage when Anzor Mekvabishvili drove a low shot past the far post in the 57th minute.
Georgia saw their advantage wiped out just moments later as substitute Lingr headed a near-post corner against the upright, before the ball bounced off Schick and into the awaiting net.
Czech Republic then went agonisingly close to completing the turnaround from another corner, but the towering Ladislav Krejci could only send his header wide of Mamardashvili's goal.
As the contest drifted into the final 15 minutes, Mamardashvili was required to make another stop, diving down low to his left to push Lingr's driven shot away from goal.
Georgia may have looked weary, but they still had enough energy to carve out the game's final chance in the fifth minute of stoppage time.
A dangerous counter-attack culminated with the ball being worked to Lobajanidze, who had only Stanek to beat when he launched his right-footed strike into the stands and in the process, he spurned the chance to claim Georgia's first win at a major tournament.
Patrik Schick gets the equaliser! #GEOCZE #BBCEuros #Euro2024 pic.twitter.com/a1qeG9AWVx
— BBC Sport (@BBCSport) June 22, 2024
Man of the Match - Giorgi Mamardashvili
Mamardashvili is one of the main reasons why Georgia left the Volksparkstadion with a point, even if it may not be enough in the grand scheme of things.
The 23-year-old made several early stops to prevent his side from getting off to a poor start, before making more important saves in the second half to frustrate Hasek's troops.
In total, Mamardashvili made 11 saves throughout the course of the contest, while he also dealt with a number of crosses to help alleviate the pressure on his defence.
What next for Georgia and Czech Republic?
Having collected just one point from their first two matches, Georgia and Czech Republic will both have to win their final games to have any chance of reaching the last 16.
Czech Republic will prepare for Wednesday's clash with Turkey, while the major tournament debutants will be tasked with pulling off a major upset against Portugal.
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