Milan Baros had the hosts' best chance of the match five minutes before half-time but could not make contact with Daniel Pudil's cross.
Thomas Hubschman was sent off for a wild challenge on Alonso with 21 minutes remaining and the Czechs were thankful to Petr Cech for keeping the score down in the final stages.
Spain boss Vicente Del Bosque had started with the Premier League trio of Mata, Silva and Fernando Torres and it took only six minutes for that decision to pay dividends as a wonderful pass from Xavi found Mata with only club-mate Cech to beat and he did so with a calm left-footed finish.
The world champions were dominant in possession in the early stages and were content just to keep the ball for long periods, but had not created another clear-cut scoring opportunity before the second goal arrived after 23 minutes.
Referee Paolo Tagliavento played a good advantage as Torres was fouled out on the right but Silva picked up the loose ball and drove into the area before laying the ball back to the edge of the box for Alonso to stroke home his 12th international goal.
Xavi nearly added a third on 35 minutes but his free-kick floated just over the crossbar before the Czechs passed up two good opportunities to get one back before the break.
Tomas Rosicky shot wide after being found by Baros' cut-back from the left, before Baros himself somehow failed to make contact with Pudil's cross when completely unmarked only eight yards out.
Carles Puyol had been brought on to replace Sergio Ramos at half-time and the Barcelona captain was lucky to stay on the field 10 minutes into the second half as he appeared to block Baros as the Galatasaray striker ran through on goal but Tagliavento waved play on.
The only downside of an extremely positive evening for Del Bosque was the performance of Torres who again seemed far from his best before being replaced by David Villa on the hour mark.
The hosts were then reduced to 10 men as Hubschman was shown a straight red card for a horrific lunge on Alonso which fortunately for the Real Madrid midfielder did not appear to cause a serious injury, although he was replaced by Javi Martinez as a precaution.
Villa nearly had his 50th international goal but his lob over Cech landed on the roof of the net before Martinez was denied his first goal at senior international level by a wonderful save from the Chelsea goalkeeper.
Martinez's deflected shot struck the bar with 10 minutes remaining as Spain cruised to their 13th straight victory in competitive internationals.