Rangers made most of the early running on the left flank with Matt McKay combining well with Jelavic as they sought a way round the back of the Saints’ defence.
Jelavic was at the centre of most of the best moments for the Light Blues in the first half, and there would have been concern when he was treated for a bloody nose just after the ten minute mark.
He quickly returned to the action though and he produced the standout moment in the first period a little less than ten minutes later.
His superb chest control knocked the ball in to the path of Steven Davis who, when he couldn’t work room for a shot, returned the ball to the Croatian front man.
It took some excellent last ditch defending from two Saints men to block his shot and the chance was lost.
It was, in truth, the only really dangerous moment of the opening half for the home side, and although they looked comfortable throughout they rarely threatened to open up the visitors.
With McKay on the left and Alejandro Bedoya on the right there were attacking options across the midfield.
And it was when Bedoya broke beyond the forward line that he looked most dangerous.
In the 21st minute he almost got on the end of Jelavic’s cross when he burst forward, but his run was just short of the Croatian’s delivery.
The lack of chances was frustrating the home crowd, but not to the same degree as some of the officials’ decision.
The Ibrox support clearly felt a number of calls went against them and things on and off the pitch were becoming increasingly heated as half time approached.
The mood of frustration was not helped early in the second period by a series of self-inflicted problems for the home side.
In the 47 minute Goian and Bocanegra did well to clear but the ball broke to Murray Davidson and the midfielder cracked a shot toward goal that McGregor watched sail by.
The Rangers keeper was then called in to action three minutes later when his defence were hit by indecision and he had to tip a cushioned header over the top.
That might have kick started a Rangers response but all too often they resorted to a direct route and couldn’t find a way through with the aerial approach.
When Lafferty’s free kick on the hour mark trundled past the wall and almost found Bedoya it was the signal for McCoist to make changes.
McKay was withdrawn and with the introduction of John Fleck there was a change in shape.
The young midfielder did well when he was found with space, but Rangers managed to do that all too infrequently.
Kane Hemmings was then introduced for Bedoya as Rangers looked for another way through but the young forward got little in the way of chances on a frustrating afternoon for the home side.