The result leaves the Light Blues with a mountain to climb in the title race as they now trail Celtic by seven points.
Today's performance by both sides was frankly poor. Rangers dominated play - indeed Celtic scored with their first real attack - only for the lack of a cutting edge to prove costly for the home side.
Manager Walter Smith made one change from last week with Charlie Adam replacing Kyle Lafferty.
The visiting fans in the Broomloan Road Stand were polluting the atmosphere prior to kick-off with sickening racist and sectarian chants and songs in support of terrorist organisations - but of course one should not be surprised as this is a club who cannot trust their support to honour Remembrance Sunday.
Rangers had a strong penalty claim in five minutes for handball against Gary Caldwell but to no-one's surprise Referee Craig Thomson turned a blind eye as Steve Davis shot wide from the rebound.
Five minutes later Kenny Miller skinned Andreas Hinkel wide on the left - but when his cross found Kris Boyd the striker was sluggish in his reaction and the chance was lost.
The resultant Davis corner saw Kirk Broadfoot bundle the ball home only for the referee to disallow the effort for an alleged foul on Artur Boruc.
Rangers were in command - but another chance went begging in 28 minutes when a long clearance from Allan McGregor, head-flicked on by Boyd, released Miller through on goal only for the forward to shoot over.
A less than memorable first-half ended goalless.
Boyd should have broken the deadlock immediately after the restart when he was through on goal from a superb Barry Ferguson pass only to shoot straight at Boruc.
Sixty seconds later Georgis Samaras blatantly shoved Ferguson off the ball - but again Craig Thomson, demonstrating his true colours, contented himself with a lecture.
The turning-point of the game arrived in 54 minutes when Miller, through on a Ferguson lob, was hauled down on the edge of the box by Caldwell. Without question it should have been a straight red card for the denial of a clear goalscoring opportunity - but the referee incredibly produced only yellow.
Boyd wasted the effort by driving the ball straight at the wall, with both Mendes and Adam surely better options.
Celtic broke from the resultant corner in 57 minutes for Samaras to head-flick the ball on to McDonald who swivelled just inside the box to volley home from fifteen yards with Broadfoot badly at fault in allowing him the time and space to turn.
Four minutes later Lafferty replaced Adam, although for many 'Gers fans there were more obvious candidates to be taken off with Boyd and Miller most prominent.
At the same time Darren O'Dea substituted for Koki Mizuno, the Japenese youngster having been effectively nullified by Adam to the extent that Celtic Manager Gordon Strachan had switched him over to the left.
Craig Thomson again influenced the game in 69 minutes when Lee Naylor committed a shocking foul on Steven Whittaker. The Celtic dfeender had already been booked and this tackle was certainly worthy - at the very least - of a second yellow card - but the referee simply got around this by awarding a throw-in.
Whittaker was so badly injured that he was replaced five minutes later by Nacho Novo.
Paul Hartley tested Allan McGregor with a thirty-yarder that the goalkeeper held - but Celtic were by now time-wasting expertly as they adopted an ultra-defensive mode.
Rangers were unable to break through, with Boyd at his ineffective best, demonstrating exactly why he should NOT play in these games.
Afterwards a crestfallen Walter Smith lamented:
"I was disappointed to lose. We were the better side until the goal, but then lost our composure. There's no margin for error now. We will keep going and look to bounce back."
Meanwhile Gordon Strachan was honest enough to admit:
"Either side could have won."
RANGERS McGregor; Whittaker (Novo 74), Weir, Broadfoot, Papac; Davis, Mendes, Ferguson, Adam (Lafferty 61); Boyd, Miller
UNUSED SUBS McCulloch, Dailly, Alexander, Aaron, Fleck
CELTIC Boruc; Hinkel (Wilson 45), Caldwell, McManus, Naylor; Mizuno (O'Dea 61), Hartley, S. Brown, Robson; Samaras, McDonald (Vennegoor of Hesselink 90)
UNUSED SUBS Hutchinson, M. Brown, Loovens, Crosas
Referee Craig Thomson