Dan James powered in a dramatic late header to settle this qualifier on a fiery night in Cardiff as both sides ended with ten men.
Manchester United winger James might be small in stature but he rose superbly to head in on 81 minutes.
James’ fourth international goal sealed victory with the first headed goal of his career from skipper Gareth Bale’s excellent left-foot curling cross.
It capped a dramatic night as first Connor Roberts went down pole-axed after Patrik Schick pushed him in the throat and was shown a straight red after the break.
The hosts then ended up with 10 men themselves when Tomas Soucek helped earn Roberts a second booking in the 77th minute.
But Wales still prevailed after some brilliance from Bale and James, plus plenty of gutsy last-ditch defending.
Centre-backs Joe Rodon and James Lawrence in particular both produced goal-saving interventions in the second half.
It ensured Wales won 1-0 for the sixth time in 11 games.
Victory also boosts caretaker Rob Page’s prospects of succeeding absent boss Ryan Giggs who is on police bail and might not return for the Euros.
Page made some bold substitutions to go for the win and was rewarded late on.
The points keep Wales firmly in the hunt for second place in the group assuming world No.1 ranked side Belgium win it.
It also vindicated Page’s hardline approach to send home Rabbi Matondo, Tyler Roberts and Hal Robson-Kanu for breaking a hotel curfew in the build up.
Page, who saw Wales lose their opening qualifier to Belgium, reflected: “We found the way to win, we knew we were in for a battle and they were a threat constantly.
“They had six up front at times and a massive aerial threat in the box.
“If a crowd would have been here, that goal, everyone would have been buzzing.
“In the 90 minutes I think we had the clear cut chances and thankfully we took one at the end.
“Three points so far is a great return considering the players not here, you bring those players back and there are bigger and better things to come.”
The visitors included Slavia Prague’s Ondrej Kudela despite police investigating an alleged racist row with Rangers Glen Kamara earlier this month at Ibrox.
Unlike Wales, the Czechs opted not to take the knee before kick-off and instead pointed to the UEFA Respect inscription on the sleeve of their shirts.
They made a positive start as Jakub Jankto had three efforts in the opening 15 minutes.
Yet it was Wales who went closest to opening the scoring in the 36th minute.
Neco Williams swung over a superb inswinging cross from the left which Bale met at the backpost on the volley.
But his effort into the ground bounced up for keeper Tomas Vaclik to make a superb reaction.
Wales also appealed in vain for a penalty before the break when James went to ground in the box after surging in before being challenged by Soucek.
After the break Schick received his marching orders as Roberts undoubtedly made a meal of it.
But despite their numerical advantage , Wales still needed a superb covering tackle by Lawrence to clear from Lukas Provod.
Then there was an huge irony to Roberts himself getting ordered off for a second booking after Soucek went down.
Record scorer Bale was unable to add to his 33 international goals and it is now nine games without scoring since October 2019.
But the Real Madrid ace, on loan at Spurs, still provided a moment of pure quality to help settle the clash.
Page added: “The cards changed the game.
“Then we had Connor Roberts sent off and had to shuffle again so it was a squad performance.
“Defenders pride themselves in those sort of performances, they would have enjoyed those last few minutes, and Joe Rodon’s block at the end is as good as a goal.”
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