Gavi, aged 17 years and 304 days, became the youngest ever player to score for Spain as he curled in to cancel out Jakub Pesek's fourth-minute opener in Prague.
The Barcelona midfielder's strike also meant Spain has scored in 16 straight games in all competitions, only twice achieving such longer streaks in history.
Jan Kutcha then again edged Czech Republic ahead in the Nations League encounter as he chipped over the onrushing Unai Simon in the second half.
But there was to be late drama as Inigo Martinez's 90th-minute header snatched a point for Spain, which sits two points behind Group A2 joint-leaders Czech Republic and Portugal after two games.
With just one team progressing to the Nations League finals, Luis Enrique was glad to pick up a point but urged his side to improve.
Asked whether the stalemate would keep the critics quiet, the Spain coach told reporters: "Noise is the most beautiful thing in the world of football. I know what I play, I know where I'm going.
"There are many things to improve. But the best thing about drawing is that the rival does not add three points.
"The important thing is that the rival does not escape us."
Luis Enrique was also quick to heap praise on teenage star Gavi after yet another fine performance in midfield.
"I know Gavi very well, I've been watching videos for five years of him. If there was any player who we wanted in that position in the first half, it was him," he said. "Either he shoots or he gets into the area, and that conviction is unstoppable."