The Netherlands were looking to take advantage of Germany's surprise 0-0 draw with Latvia and goals from Wilfred Bouma and Ruud van Nistelrooy gave them a flying start. After Baros had restored parity, Dutch defender Johnny Heitinga was sent off and the 10-man Dutch were caught with a sucker punch in the 88th minute when Smicer tucked home Karel Poborsky's cut-back.
"Heitinga's sending-off was stupid," said Advocaat. "A young player must know never to tackle like that when he already has one yellow card."
The Netherlands are third in the group with a single point, one behind Germany.
The Dutch made two changes to the team that drew 1-1 with Germany. AC Milan midfielder Clarence Seedorf and Chelsea winger Arjen Robben both returned after recovering from injury to replace Rafael van der Vaart and Boudewijn Zouden.
The Czechs made one change with central defender Martin Jiranek coming in for the fever-stricken Rene Bolf.
Beaten finalists at Euro 96, the Czech Republic almost had the perfect start in the second minute, Tomas Rosicky's chip over the Dutch defence finding Koller unmarked but the towering striker volleyed over the bar.
The Czechs were made to pay for Koller's miss two minutes later.
Robben's free-kick from wide on the right found the unmarked Bouma who headed low past goalkeeper Petr Cech. Seedorf shot narrowly wide after receiving a yellow card before the Dutch extended their advantage.
The lively Robben peeled off to find space on the left and delivered a low cross to the edge of the six-yard box for van Nistelrooy to slide home with ease.
A terrible mistake by Phillip Cocu allowed the Czechs back into the match four minutes later.
The Barcelona midfielder, making his 81st international appearance, gifted possession to Baros and the Liverpool striker ran at the Dutch defence, evaded two challenges and set up Koller for an easy tap-in.
The Netherlands' early confidence quickly evaporated but they recovered their composure and almost snatched a third before half-time when Edgar Davids' fierce angled drive hit the post.
Poborsky was denied an equalizer two minutes after the break when Edwin van der Sar blocked his shot with his leg. Smicer almost brought the Czechs level, a superb fingertip save from van der Sar keeping his team's lead intact.
The Czech always looked threatening on the break and a raid upfield saw them level in the 71st minute. The outstanding Nedved's left-wing cross was chested down by Koller for Baros whose rising half-volley gave Van der Sar no chance.
Heitinga's dismissal hindered Dutch chances of a recovery.
The Dutch must beat Latvia on Wednesday to have any chance of qualifying.
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