Jake Gyllenhaal -- HOSPITALIZED .. Stitches After Punching Mirror

Jake Gyllenhaal socked a mirror on the L.A. set of his new movie -- slicing up his hand so badly, he was rushed to the hospital to be stitched up.

It all went down Wednesday morning, according to People.com ... Jake "flipped out" during a scene for "Nightcrawler" and punched the mirror with his fist, shattering it and damaging his hand in the process.

Jake was reportedly taken to a nearby ER where he was treated and released. He returned to the set later that day.