Croatia clung to their early lead as the hosts pushed to level, and the drama came late. The Czech Republic found an equaliser in the closing minutes. Croatia answered inside two, Mayer stealing the winner to bank three precious points.
Croatia wasted no time. They caught the hosts cold after just two minutes, Ivan Perisic latching onto a slick counterattack and firing straight into the net.
Pjetrina threaded the pass, Perisic found space on the right, and his strike beat the goalkeeper to hand Croatia the early lead.
That goal gave them both a mental and tactical edge. They dictated the tempo, pressing high to win the ball back quickly and shifting fluidly through midfield in search of a second.
The Czech Republic looked rattled by the early blow and took time to settle, before gradually working their way back into the game through movement on the flanks and crosses into the box.
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Threatening Livakovic's goal proved beyond them, their attempts lacking the needed accuracy, while Perisic kept tormenting the Czech defence out wide without adding a second.
Croatia went close to extending their advantage more than once. The clearest fell to Gvardiol from close range after a corner, when he tried to flick the ball goalwards with his heel only for the goalkeeper to block, before a second chance went begging from the rebound.
Loud appeals followed for a penalty when Perisic tumbled inside the area after a collision with a defender, but the referee waved play on, and Croatia's slender 1-0 lead held until the break.
The Czech Republic come back, and Mayer responds quickly
From the restart the Czech Republic lifted the tempo and leaned harder on Croatia's defence, using the movement of Hlozek and Hubi, yet the final touch remained their biggest stumbling block.
Croatia refused to sit back. They kept hunting a second through counters and wide play, coming close on more than one occasion.
Matanovic nearly made it two. Taking the ball on the left, he drove towards the box and lashed a low effort at the near post, but the Czech keeper stood firm.
Kovacic also tried his luck from the edge of the area, though the shot reached the goalkeeper comfortably, and Matanovic squandered another close-range opening after the defence cleared before the ball could reach the net.
As the clock ran down, the Czech Republic threw everything at an equaliser and finally breached Livakovic's goal in the 84th minute.
Hlozek was the man. His first shot was blocked, but he pounced on the rebound, teed it up on his left foot and rifled it into the far corner, sending the stands into raptures.
The joy was fleeting. Croatia hit straight back just two minutes later, Mayer firing home the winner in the 86th minute.
Mayer found space inside the box, took the ball in a perfect shooting position and steered it precisely into the far corner, restoring Croatia's lead and gutting the hosts at the cruellest moment.
The Czech Republic went again in the dying minutes, but Croatia saw it out, and the final whistle confirmed a 2-1 win for the visitors in a contest settled by fine margins and clinical finishing.
The group situation after the match
Victory lifted Croatia to 6 points and third place to close out their group campaign, while the Czech Republic finished pointless at the foot of the table and dropped to the second tier.
England and Spain booked their quarter-final spots. England topped the group on 15 points, edging Spain on goal difference after both finished level on points.
Croatia walked away with a telling moral victory, proving they can handle the tight moments. The Czech Republic took a bitter blow, so close to snatching a point before Mayer ruined the party with a killer goal.
