American international Edu gave Scottish champions Rangers the lead 11 minutes before half-time only to head into his own net just after the interval.
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Unai Emery's Valencia dominated the remainder of the game but could not find a way past a typically stubborn Rangers defence.
With Valencia on four points and Rangers on five, the return fixture between the two sides in Spain next month will go a long way to deciding who will progress to the last 16. Manchester United lead with seven points while Bursaspor are pointless.
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Valencia controlled possession from the start but when Walter Smith's side did venture forward they caused problems and Steven Naismith would have given them the lead if he had managed to connect to Kenny Miller's cross.
The hosts did move ahead in the 34th minute when Edu rose above Cesar Sanchez to head in from a Vladimir Weiss corner.
The midfielder then hit the post from 25 yards, with Miller failing to get the follow up on target despite Sanchez being stranded.
Rangers's advantage was wiped out less than a minute after the break when Juan Mata clipped in a free kick and Edu glanced a header into the corner of his own net as Rangers conceded for the first time in the Champions League this season.
As the visitors piled forward, Mata lifted a shot over the bar from the edge of the area and Pablo Hernandez had a close range effort deflected onto the roof of the Rangers goal.
The impressive Steven Davis had a lob touched over by Sanchez who then saved from Naismith.
