كتب : Hatem Maher
Ciprian Marica put the German side ahead after five minutes with a close range header and Christian Traesch doubled the advantage three minutes later.
Russian striker Pavel Pogrebnyak added the third on 11 minutes after a fine individual effort.
Unirea narrowed the gap with a goal from Antonio Semedo early in the second half but Stuttgart held on for a valuable win.
Stuttgart moved ahead of Unirea, who have eight points and will play in the Europa League, on nine points in Group G.
Already-qualified Sevilla, who progressed as the group winners, defeated Scottish side Rangers with a penalty from Malian striker Fredi Kanoute.