Rangers, already assured of coming third and taking a Europa League spot, went ahead after a rare attack in the 19th minute with Kenny Miller driving home a shot from a left-wing cross.
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Bursaspor dominated possession but failed to translate that into chances until Sercan Yildirim whipped up the enthusiastic home support by firing in a cross from Ozan Ipek in the 79th.
"It was a good end to our campaign. We played good football and exerted a lot of pressure and created scoring opportunities in the second half," said Bursaspor coach Ertugrul Saglam.
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"It was a match we should have won and we should be disappointed that we only drew," he added.
Rangers had to survive an intense period of pressure in the last 10 minutes as Bursaspor went in search of a victory.
Sercan had a golden chance to win the game in the 86th minute when he beat one defender on a run into the box, but he lost control of the ball with only the keeper to beat.
Both teams had already been eliminated from the Champions League before Tuesday's match, with Manchester United on 14 points and Valencia (11) going through from a tough group.
Rangers finished with six points and Bursaspor on one.
Bursa's preparations for the match had been overshadowed by trouble between their fans and those of Istanbul's Besiktas at a domestic league match on Sunday.
Several people were stabbed in a mass brawl ahead of the game.
