Luis Enrique vowed to rotate after Spain's opening Group A2 stalemate with Portugal and made eight changes in Prague, where Jakub Pesek struck after just four minutes.
Kuchta nudged Jaroslav Silhavy's side ahead again in the second half after Gavi's first-half equaliser, before Martinez popped up in the 90th minute to snatch a point.
The stalemate left Spain three points Group A2 joint-leaders Czech Republic and Portugal, which eased past Switzerland.
Spain boasted 80 per cent of possession in the opening 15 minutes but found themselves behind after Pesek tapped in Kuchta's selfless square pass, with a VAR check for offside allowing the goal to stand.
Pablo Sarabia skewed a presentable opportunity wide as Spain searched for a response, which arrived when Gavi curled a precise finish low into Tomas Vaclik's right corner.
Luis Enrique introduced Ferran Torres at half-time but it was fellow winger Dani Olmo who almost put Spain ahead after the interval when he whipped narrowly wide.
Kuchta then rolled a glorious opportunity wide when one-on-one with Simon, while Marco Asensio drilled a left-footed attempt against the right post at the other end.
But Kutcha nudged the hosts ahead as he latched onto Vaclav Cerny's incisive throughball before coolly chipping the onrushing Simon.
Torres headed onto the post minutes later before Spain stole a late point as Martinez headed in Asensio's cross via the underside of the crossbar.