Predrag Krunic's Oldenburg team won 89-82 to finish 3-3 in Group J but Virtus BolognaFiere's triumph at BC Kyiv earlier in the night left both Virtus and Kyiv in the last eight with 4-2 records.
Galatasaray led for much of the game but EWE Baskets never let them pull away.
After Quinton Hosley's basket for Galatasaray snapped a 74-74 tie, EWE Baskets' Jasmin Perkovic answered with a three-pointer.
Jason Gardner then followed with a three-point play for the Germans before Rickey Paulding capped the 8-0 run with two free throws for an 82-76 advantage.
Galatasaray (1-5) reduced the arrears to five but got no closer.
Je'Kel Foster scored 26 points, Paulding 18 and Gardner 14 for EWE Baskets, who were 13 of 29 (44.8%) from long range.
Foster was a scintillating six of eight (75%) from behind the arc.
Anthony Tolliver poured in 25 points to lead Galatasaray.