The victory for Spain, who have taken all 21 points from their seven matches and had already qualified for the finals, has left the Czechs just two points ahead of Scotland.
However, they have played a game more than their play-off rivals and must hope the Scots, who visit Liechtenstein on Saturday and Spain next Tuesday, drop points.
Czech coach Michal Bilek is counting on the Spaniards putting on a similarly impressive performance against Scotland saying: "We hope Spain will play well like here."
World champions Spain took an early lead when Mata latched onto a through-ball and slotted past goalkeeper Petr Cech and they doubled their advantage after 23 minutes when David Silva found Xabi Alonso unmarked in the box to score.
The Czechs had few chances and put themselves under more pressure in the 67th minute when Tomas Huebscham was sent off for a rough tackle on Alonso who had to leave the pitch.
Spain coach Vincente del Bosque said: "It was a hard challenge and an unnecessary one. It made no sense going in for the ball like that. I don't think he [Alonso] has anything serious. It seems like a knock and nothing more."
Del Bosque told Spanish television his team had soon got into their stride but took their foot off the pedal a bit after building the early lead.
"We played well and got into a rhthym quickly," he told reporters. "Later on we relaxed a bit but in the first half when we had to play well we did so pretty effectively."
The victory marked the 13th consecutive win in competitive fixtures for Spain since they lost 1-0 to Switzerland in their opening game of last year's World Cup finals in South Africa.
Spain striker Fernando Torres started the game but had a quiet night and was unable to end his international goal drought. He came off in the second half for David Villa.
