The visitors scored a goal in each half with Yilmaz heading home before the break and Erding capping off a brilliant win in the late on, curling a left-footed shot into the net from inside the penalty area.
Pre-match favourites Romania failed to fulfil expectations throughout as interim coach Fatih Terim, in his third spell in charge of the national side, continued to inspire his Turkey team.
The vital win extends Turkey's unbeaten run to four matches in qualifying and keeps them in the hunt for a play-off spot behind runaway Group D leaders the Netherlands Holland, who qualified thanks to their 2-0 win against Andorra and Romania's loss.
Romania do have the easier run-in compared to Turkey. Victor Piturca's men play Andorra and Estonia in their final two games and will still be hopeful of reaching the World Cup.
The hosts made two changes from the side that beat Hungary 3-0, with midfield duo Ovidiu Stefan Hoban and Cristian Tanase replacing Alexandru Iulian Maxim and the suspended Alexandru Bourceanu.
Terim, meanwhile, replaced Nuri Sahin with Selcuk Inan to bolster a four-man midfield.
The first chance of the game came in the sixth minute when Mihai Doru Pintilii took advantage of some lax Turkish defending to sneek in behind, but his weak cross was deflected out by goalkeeper Volkan Demirel.
The visitors responded minutes later, though, through Yilmaz, but the 28-year-old, under the close attention of the Romanian defence, side-footed his effort at the goalkeeper.
But Yilmaz made up for his miss in the 22nd minute when he rose above two Romanian defenders to head home and give Turkey a surprise lead. The makeshift forward stood his ground to glance Caner Erkin's wonderful cross past Ciprian Anton Tatarusanu's outstretched palm.
Piturca made two substitutions after the interval, choosing to bring on Adrian Popa and Iulian Maxim as he tried to search for a way back into the match.
Turkey, though, could have easily been 2-0 up if Umut Bulut had been aware of how much time he had with only Tatarusanu to beat after he had been put through by Gokhan Tore.
Instead, the 30-year-old meekly hit his shot at Tatarusanu, even though he had team-mates in support.
Popa hit the post with a right-footed drive after 68 minutes as Romania pushed for an equaliser and Dorin Golan directed a late head straight at Demirel from a free-kick.
Late substitute Erding then hit the second in injury-time when he evaded the raised legs of Romania's centre-halves to fire the ball home.
