Still, Rangers maintained their grip on the game.
Dessers flicked to Bajrami who, in turn, brilliantly sent Vaclav Cerny clear in on goal in acres of space. He had to score. He didn’t, as the ball flashed just past the post.
That became a theme, glaring missed chances, until late on.
Dessers fed Bajrami racing into the box. It was another glorious chance until, incredibly, it wasn't.
The Albania international, seemingly full of confidence after his goal, inexplicably didn't shoot, reversed it back towards the striker and the chance was gone.
Malmo emerged re-energised after half-time, firing crosses into the penalty area and shots from distance. Yet Rangers stood firm under that pressure.
Anders Christiansen fired over on the run, but that was Malmo's best chance. Few tested Butland at all in truth.
Rangers still continued to threaten and Dessers had another glorious chance to end it but fired high and wide when he had to score from close range.
They got there, though. Substitute Ross McCausland stepped up late on with a crisp, low strike to secure a crucial win that gets Rangers' Europa League campaign off to an excellent start.