Walter Smith's men had failed to register a win in European action since they beat Fiorentina en route to the 2008 UEFA Cup final, with last years' efforts in the Champions League a particular sore point.
Rangers shipped 10 goals at home and failed to pick up a single point in front of their own fans as they finished bottom of the section.
But they went some way to exorcising those demons by claiming three points against the Turkish champions to add to the draw they earned against Manchester United at Old Trafford in their Group C opener.
Kirk Broadfoot and Maurice Edu were added to the starting line-up from the weekend win at Aberdeen, with Vladimir Weiss dropping to the bench and Nikica Jelavic ineligible for the competition. Steven Davis was passed fit after fears over a hamstring strain.
Boss Walter Smith had warned of the importance of not losing the first goal and Rangers tried to apply some early pressure, Edu coming close with a shot from the edge of the area that deflected just wide of the post.
Naismith then won a free-kick, which was curled into the box by Davis and cleared as far as Madjid Bougherra. However, his effort dipped well over the crossbar after clipping a Bursaspor defender.
The breakthrough came after 18 minutes when Steven Whittaker's cross from the right was met by Broadfoot and his header was collected by Naismith, who sidefooted home from six yards.
Bursaspor had tried their luck with a couple of half-chances which did little to trouble Allan McGregor in the Rangers goal but he was called into action to tip Gokcek Wederson's free-kick just over the bar as the Turks tried to haul themselves back in the game.
At the other end, Naismith could have added to his tally on the night when he ran on to a lovely pass from Davis - only to see his volley swerve past the upright.
Kenny Miller has netted 10 goals in six SPL games so far this season and could have claimed his first in the Champions League had he been more clinical in front of goal after the restart.
Edu was the provider and the striker found himself with only the goalkeeper to beat but Dimitar Ivankov managed to block and Naismith blasted the rebound well over.
Edu then had a chance at goal himself when he met a cutback from the byline from Lee McCulloch, only to drive inches wide of the target from just inside the box.
The final minute saw Ali Tandogan stand over a free-kick for Bursaspor in what was a tense moment for the home side - but Rangers managed to clear the ball up the park as time ran down on the clock.
In the end, the Scottish champions were able to hold on for a win which allows the Ibrox faithful to head home in the hope of a better Champions League campaign this time around.