The unmarked Gyurcso latched onto a long-range pass in front of goal and rifled a shot past goalkeeper Petr Cech.
Hungary opened the scoring after just six minutes when Balazs Dzsudzsak's quick free-kick from just outside the penalty area caught the Czechs out as they organised their defence.
The hosts, who created several chances, equalised with a Michal Kadlec penalty midway through the first half after forward Milan Baros was dragged down inside the area.
Czech Republic coach Michal Bilek fielded a full strength side except for injured captain Tomas Rosicky, although the midfielder is expected to be fit for the tournament.
Bilek said the Czechs could not find the final pass to penetrate a physical Hungarian side who spent most of the night concentrating on defending rather than looking to attack.
He also lamented the two defensive breakdowns that gifted the visitors their two goals but said the Czechs would be ready for the tournament which starts next week.
"The result will not affect our confidence," Bilek told a news conference. "We dominated the game but could not get over the [defensive] wall."
The Czechs, semi-finalists in 2004 and finalists in 1996, play Russia on June 8 in their opening Group A game before facing former European champions Greece and co-hosts Poland.
