Substitute Nicolas Pepe thought he had earned the Gunners a slender quarter-final first-leg advantage when he broke the deadlock in the 86th minute.
But Tomas Holes headed home in the dying moments of the game from close range to give Slavia Prague a precious away goal.
The second leg in Prague takes place next Thursday (20:00 BST).
Gunners have it all to do
Gunners boss Mikel Arteta stated he was in “shock” after his side’s tame 3-0 surrender to Liverpool last weekend, a performance which brought stinging criticism from both fans and pundits.
He reacted by making six changes – three of which were forced – to his starting line-up, with captain Pierre-Emerick Aubameyang the most high-profile casualty.
Asked about his decision to leave the Gabon forward out, Arteta said he had to pick the “right team to start the game in the best possible way”.
Aubameyang, who has 13 league and cup goals for his club this season but none since 6 March, cut a frustrated figure as he watched Willian, from a free-kick, clip the outside of the post before Alexandre Lacazette raced through, only to hit the bar.
Aubameyang was finally sent on after 78 minutes and made an impact as his pass allowed Pepe to race into the box and produce a composed finish past keeper Ondrej Kolar.
But Arsenal failed to see the game out and Hole’s back-post header means Arteta’s side have it all to do against the 2019-20 Czech champions in a week’s time.