The returning Aaron Ramsey gave Wales a 36th-minute lead, although that was quickly wiped out by Jakub Pesek after Ward had failed to gather Filip Novak’s shot.
Ward was left even more red-faced four minutes after the restart after miscontrolling Ramsey’s backpass and getting the final touch on the Czechs’ second goal.
However, Daniel James secured the point Wales more than deserved in a thrilling contest.
The draw leaves Wales and the Czech Republic locked on eight points behind runway group leaders Belgium – and the Dragons still have a game in hand on their rivals.
Wales were without talismanic captain Gareth Bale who had suffered a serious hamstring injury since the last international camp.
Bale, Wales’ all-time record goalscorer, was the only player to register in the Dragons’ previous five games with a match-winning hat-trick against Belarus.
But the visitors were bolstered by the return of Kieffer Moore and Ramsey, with the Juventus midfielder taking the armband in Bale’s absence.
Cardiff forward Moore was the only player in the Wales starting line-up to score this season – and that was nearly two months ago on August 14.
Wales had beaten the Czechs at home in March to strike a blow in the battle for second place, and knew that defeat in Prague would probably leave them relying on their 2020 Nations League results for a place in March’s World Cup play-offs.
Czech Republic were without injured West Ham defender Vladimir Coufal but Patrik Schick, who was joint top-scorer at this summer’s Euro 2020 as Jaroslav Silhavy’s side reached the quarter-finals, was back to lead the attack.
The Wales players made their usual pre-match stand against racism by taking the knee and were roundly booed by home fans.
Wales boss Robert Page had opted for a 3-5-2 formation with Moore and James up front and Ramsey offering swift support from an advanced midfield position.
Ramsey made his presence instantly felt by clattering into Novak after 13 seconds to earn a yellow card.
Wales escaped when Ward pushed out Pesek’s low drive and Neco Williams completed the clearance.
But Wales – and Ramsey in particular – continually probed and threatened throughout an entertaining first half.
A mix-up in the home defence allowed James to advance before skying wide and an even better chance arrived after 18 minutes when Ramsey released James and Wales wasted a two-on-one opportunity – James dithered before finding Moore, who was still favourite to beat the onrushing Vaclik but failed to do so.
Schick’s deflected effort looped over the bar before Wales scored from the resulting Czech Republic corner.
Ethan Ampadu led a rapid break and Williams played his cross into a dangerous area. James failed to get a touch on the ball, but Ramsey was racing in behind and he sat down Vaclik superbly before tucking away his 18th international goal.
The lead lasted barely more than a minute as Novak broke beyond the Wales defence and Ward pushed out a shot that might have been straying wide.
Williams slipped at the wrong moment and Pesek pounced in front of a gaping goal.
Worse was to come for Ward with his loss of concentration ending up with him touching the ball onto the post. The Leicester goalkeeper desperately tried to retrieve the situation but both he and the ball ended up in the back of the net.
Wilson slipped in James and his excellent lofted finish beat Vaclik and survived a VAR review.
Moore and Ramsey almost won it for Wales late on, but a furious contest ended all square with the race for second place set to go down to the wire.
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