The win at the Dr. Constantin Radulescu Stadium spoiled Paulo Sergio's European debut as coach of Cluj while Galatasaray revived their chances of reaching the last 16 in Europe's elite club competition.
Group leaders Manchester United have 12 points from four matches and have already reached the knockout stage. Galatasaray and CFR Cluj are on four, with Braga on three.
Yilmaz opened the scoring after 18 minutes when he headed into the top corner of the goal from Hamit Altintop's precise right-wing cross.
Senegalese winger Modou Sougou, making his first appearance for Cluj after a three-week absence due to injury, made it 1-1 eight minutes after the break with a cool finish, with substitute Rafael Bastos providing a delightful assist.
Yilmaz's deadly finishing stole the show, however, as the tall Turkey international netted twice within 14 minutes with an easy right-footed shot from close range and then a calm left-footer.
The 27-year-old, who joined Galatasaray from Trabsonspor in a five-million-euro deal in July, has scored all of Galatasaray's four goals in their group matches as he hit the target in the 1-1 draw with Cluj in Istanbul last month.
Cluj next host Braga, while Galatasaray are at home against United on November 20.
