The home team's goals came early and very late. Nacho Novo gave Rangers the perfect start with a goal after five minutes, but it was not until Charlie Adam scored from the penalty spot in the final minute that the Ibrox side could relax.
Rangers could have made life easier for themselves but Kris Boyd's penalty immediately after half-time was brilliantly saved by keeper Nir Davidovitch diving to his right.
Skipper Barry Ferguson turned in a superb performance for Rangers and drove his side forward at every opportunity.
There was a pitch invasion by a fan midway through the second half who appeared to try and chain himself to the post but he was soon removed by the police.
Rangers opened the scoring when Novo raced onto Boyd's flick and his shot took a slight deflection on its way past Davidovitch.
Soon after Brahim Hemdani gave away a free-kick on the edge of the area but Yaniv Katan's free-kick was blocked by the defensive wall.
Maccbi were dangerous on the break but lacked any real finishing power.
Rangers should have gone further ahead after the interval when Dado Prso was brought down but Boyd's penalty was well saved.
Rangers made sure of the points when Ferguson broke from the halfway line before being pulled down in the box.
Adam struck the penalty home with conviction to the delight of the Ibrox faithful.