McCoist made two changes with captain Steven Davis replacing John Fleck in midfield and goalkeeper Neil Alexander back between the sticks for the injured Allan McGregor.
It was a quiet opening period for the visitors as the home side looked to get an early goal.
St Johnstone did have the ball in the net on 12 minutes but Marcus Haber was adjudged to have been in an offside position before he slotted the ball past Alexander.
Rangers almost opened the scoring themselves on 16 minutes, as a beautifully weighted pass from Davis found David Healy on the edge of the box, but his first time shot squirmed just past the right hand post.
The Light Blues took the lead with 23 minutes on the clock and it was Jelavic that grabbed the goal.
Davis played a quick free kick to the impressive Sone Aluko who charged towards the Saints penalty area.
His shot was deflected by Saints defender Mackay and the ball fell to Jelavic, who slotted the ball home from six yards out.
Rangers continued to press and another excellent run by Aluko, seven minutes before half-time had the Saints defence chasing shadows and his pass to Jelavic found the striker 12 yards out.
The Croatian looked up but his shot was saved well by the feet of Enckelman and the home defence scrambled the ball to safety.
With five minutes remaining of the first half, Liam Craig finally managed to break free from marker Bartley. His cross was met by David Robertson and he should have done better as his header didn’t trouble Alexander.
The visitors started the second half well and again Aluko and Davis were at the heart of the Light Blues best moves.
On 50 minutes an Aluko through ball found Davis at the edge of the box, but his shot was deflected away for a corner.
The Ulsterman sent the ball in and Dorin Goian rose unchallenged 10-yards from goal but David Robertson cleared the ball off the line.
For all the Light Blues’ pressure, St Johnstone equalised on 67 minutes but luck had a big part to play.
A deep Craig cross from the left was met at the back post by Haber, his header hit Carlos Bocanegra and crossed the line, leaving Alexander wrong footed in the Gers goal.
With 14 minutes remaining the Light Blues were unlucky not to re-take the lead as Lee Wallace missed a header at the back post.
Aluko played in Healy and his driven shot was parried by the Saints keeper and as the ball seemed to fall perfectly for the Scotland international but he didn’t make contact and the ball was cleared.
With 10 minutes left McCoist turned to his bench as last weekend’s goal-hero Salim Kerkar replaced Wallace. Before the Algerian got a touch, Rangers were back in-front.
An Aluko free kick was met by Saints midfielder Murray Davidson whose header smashed off his own crossbar and landed at the grateful feet of Jelavic who had the simple task of tapping the ball into the empty net.
Sorry, the gallery is currently unavailable.