Last year's finalists dominated the game from the start and opened the scoring when Soler struck from close range in the 24th minute following a brilliant pass by man-of-the-match Marco Asensio.
Third-placed Czech Republic have four points, one ahead of Switzerland, who recorded their first win in this year's competition.
Luis Enrique made nine changes to the starting lineup that beat Switzerland 1-0 on Thursday.
Making his first start for Spain since November 2020, Asensio provided the pass which Soler fired in from close range.
Spain kept threatening the Czechs and enjoyed 73% of possession but often lacked the precision to make it count. They only managed to score after Gavi came off the bench in the second half.
In the 75th minute, the teenager stole the ball and raced past two opposing players before passing through to Ferran Torres, who crossed to Sarabia. The Paris Saint-Germain midfielder was left to fire the ball into an empty goal.
"It was all perfect," Soler told TVE. "We came wanting to give those fans who created an amazing atmosphere a win and it came accompanied by a great performance.
"Ending up the group leaders is the cherry on top, so it was a great effort and a fabulous night."