Rangers kept up the pressure and Steven Whittaker flashed a shot wide from outside the box.
David Villa slotted home a penalty on the stroke of half-time after Steven Whittaker was punished for handball.
Despite performing well, his replacement Steven Whittaker is more naturally suited to playing in the right full-back position.
The game was beginning to open up and Steven Whittaker and Jelavic lifted shots over the visitors' crossbar.
The Croatian striker then got on the end of Steven Whittaker's cross but could not direct his header on target.
The second half was tense with Celtic's Fraser Forster saving from Steven Whittaker and Rangers keeper Neil Alexander denying Ledley.
Steven Whittaker came into midfield in the absence of the suspended Kenny Miller, with Lafferty moving up front to partner Kris Boyd.
Steven Whittaker's back-post cross was headed into the six-yard box by Kyle Lafferty and Boyd raced in to volley past goalkeeper Graham Stack.
And he was forced into making early substitution when Callum Davidson had to go off with an injury, with Steven Whittaker replacing the full-back.
However, lone striker Kyle Lafferty could not reach it and Steven Whittaker was penalised for a foul as he slid in at the back post.
And Boyd all but confirmed the result as he despatched Steven Whittaker's low cross into the net at the end of a neat passing move.
The second half started at a whirlwind pace, with Scottish full-backs Alan Hutton and Steven Whittaker, an early replacement for the injured Callum Davidson, involved in early attacking surges.
Steven Whittaker squandered Rangers only other chance of the first half, heading well over after being found unmarked at the back post by a Steven Davis cross.
With the game in full effect, Maguire volleyed over for Aberdeen from 20 yards after Steven Whittaker was dispossessed, much to the relief of the Rangers defender.
Falkirk were awarded a penalty four minuets into the second half when Steven Whittaker tripped McBride in the box, which resulted in a booking for the Rangers player.
Steven Whittaker arrowed a low drive into the grasp of St Mirren goalkeeper Paul Gallacher before setting up Miller for a run and shot but the striker could not keep his effort down.
The hosts were relentless in their pursuit of goals and it looked as though Aberdeen were on their way to another heavy defeat when Steven Whittaker was brought down in the box by Zander Diamond.
Steven Whittaker occupied Smith's usual left-back position in the absence of Sasa Papac, while the veteran Christian Dailly was on the right and Andy Webster came in from the cold to sit on the bench.
Rangers had three players - Steven Whittaker, Madjid Bougherra and El Hadji Diouf - shown red cards, while Lennon had a heated exchange with opposition assistant manager Ally McCoist on the touchline at the final whistle.
Steven Whittaker's header over the crossbar from Steven Davis' cross failed to worry the Zenit goalkeeper before striker Jean-Claude Darcheville was tripped by Denisov and Rangers were awarded a free-kick on the edge of the area.
In one such move, Dougie Imrie freed himself from full-back Steven Whittaker and cut the ball back for Flavio Paixao, who sent a curler from his Tweetie Pie-coloured boot to test cat-like McGregor in the Rangers goal.
If Motherwell thought their re-structured defence would be given some respite by a Rangers team in party mode, they were quickly dispelled as goalscoring full-back Steven Whittaker threatened the crossbar with a trademark drive from 25 yards.
With only two Rangers players, Steven Naismith and Steven Whittaker, called up to the Scotland squad for Tuesday's match with the Faroe Isles, most of Smith's squad will have a free midweek for the first time in several weeks.
Rangers were coming off the back of their midweek Co-operative Insurance Cup success, although Walter Smith freshened up his side by introducing Steven Whittaker and John Fleck for Sasa Papac and Steven Naismith after their semi-final victory over Falkirk.
The flashpoint involving the two men followed a match that was pockmarked by red cards for Rangers players Steven Whittaker, Madjid Bougherra and El Hadji Diouf, 13 cautions and a series of angry scenes in the Celtic Park technical areas and tunnel.
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Meanwhile, Weir was keen to draw a line under the fall-out from Wednesday's controversial Old Firm game, which featured red cards for Bougherra, El Hadji Diouf and Steven Whittaker and an angry touchline exchange between Rangers assistant manager Ally McCoist and Celtic boss Neil Lennon.
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