That means the Light Blues are now joint top of Group C in this season’s Champions League with Manchester United, who beat Valencia 1-0 in Spain.
Now a mouthwatering double-header with the La Liga side awaits Gers and they’ll go into the first match in Glasgow bursting with confidence after this success.
The Turks flew into Scotland with a 100 per cent record in their domestic league after winning it for the first time last term.
But they were short of ideas up front and the SPL title holders showed more grit, desire and temperament to see out a hugely important win.
That means they’ve ended their long wait for a continental success, a run which stretched back almost two and a half years to the 2-0 triumph over Sporting in April 2008.
Many home fans will have turned up at Ibrox expecting Smith to use a more expansive formation than the 5-4-1 shape deployed in the group opener at Old Trafford.
But after his side lost two sloppy goals in the 3-2 win over Aberdeen at Pittodrie on Sunday, it maybe wasn’t too surprising he reverted back to the defensive shape.
Indeed, Smith went with the same starting XI that featured at the Theatre of Dreams and that meant recalls for Maurice Edu and Kirk Broadfoot.
Out dropped the ineligible Nikica Jelavic, while winger Vladimir Weiss took a place on the bench.
Gers looked shaky to begin with but had the first real opportunity when Naismith released Kenny Miller with a great through pass.
But while the Scotland striker stepped away from Milan Stepanov, Omer Erdogan slid in superbly just outside the penalty area to stop him from shooting.
Buoyed by that, Edu had a go next when he found himself in space 25 yards from goal and it took the slightest of deflections to divert it from the target.
Those chances didn’t take away from the fact the hosts were nervy and Sercan Yildirim might have done better when the Light Blues gave away possession 20 yards out.
Pablo Batalla attempted to beat Allan McGregor from distance but his drive from well outside the box was always drifting past the post.
Back came Rangers and Madjid Bougherra nearly sparked euphoria when he shot after Steven Davis’ centre but another block took it over for a corner which came to nothing.
The game was swinging back and forth but neither side settled initially and it was clear both knew how vital it was to get a positive result for the sake of doing well in the group.
For all that, there had been signs the Turkish visitors could be exposed and when they were after 18 minutes, the SPL champions went in front.
Steven Whittaker fizzed a great cross-field pass from right to left as he switched the play to Kirk Broadfoot.
The big defender then sent in a perfectly-cushioned header and when Naismith threw himself at it, he was able to poke past Dimitar Ivankov from close range.
Going ahead did a lot for Gers’ morale and Naismith and Miller were both thriving against a clearly rattled away defence.
So too was Lee McCulloch, who got on the end of a Davis corner from the left and very nearly nodded in a second at the back post.
But it was to be expected that Bursaspor would hit back and when they did, Gokcek Vederson almost levelled.
Edu was penalised for an innocuous foul in midfield and when the left back took the free kick, it arrowed towards the roof of the net until McGregor expertly tipped it over.
With the interval approaching, there was an opportunity for the hosts to strike again when Vederson lost possession and Davis latched on to it.
But when he swung in for Naismith, the former Kilmarnock star really had to take the ball on the volley with a defender closing him down and he fired wide.
Bursaspor were forced into a substitution when Ivan Ergic was injured in a tackle with Whittaker and he was replaced by Federico Insua.
He almost made an immediate impact when he met a cross from the left but thankfully his header was tame and comfortably taken by McGregor.
Half-time was probably welcomed more by the Turkish champions as they had been largely disappointing in the first period.
Their manager Ertugrul Saglam chose not to make any further changes though and it was Rangers who continued to press after the restart.
Edu slipped Miller in and he got away from one man before his shot was saved by Ivankov and Naismith blazed the rebound over.
Those misses almost proved costly when Yildirim found space in the box and McCulloch eventually managed to block him.
Naismith was too high again after powerful play on the right flank by Bougherra allowed Edu to set him up.
The American was then inches away himself after he showed good footwork on the edge of the box and it seemed if another goal was coming, it would be for the Scots.
Moments later, however, there was a stark reminder that the game was far from won as Weir almost put the ball into his net from Volkan Sen’s cross with a diving header.
That chance gave Bursaspor a real lift and Sen suddenly burst into life, having another shot turned behind for a corner.
The Turks knew time was against them and they turned the screw as they tried to restore parity.
Rangers reacted to that by pushing for a second as the match opened up a lot more and Bougherra’s snap shot after Davis was denied wasn’t far off.
Moving into the final quarter of the contest, the tie was on a real knife edge as the away side began to enjoy more possession and Smith’s men tried to consolidate.
Both teams were being stretched and Ivankov had to come charging out of his box to ensure Miller didn’t get past him with an open goal to aim for.
Bursaspor knew they had to gamble and Saglam put on Turgay Bahadir and Leonel Nunez for the tiring Yildirim and Batalla.
But they were still being restricted to long-range efforts, with Vederson the architect and missing each time.
The seconds were ticking down and in truth, the visitors never really looked like finding a way back into the game.
Nevertheless, when referee Serge Gumienny blew for full time, it was to an almighty roar of relief that Rangers trooped off the park with an excellent three points in the bag.