Both clubs would have welcomed the opportunity simply to play this match after last week's Irn-Bru Third Division encounter was postponed when it emerged Elgin had sold too many tickets for the visit of Ally McCoist's men.
Rangers named an unchanged side from their last game, a win over East Stirling, for Sunday's clash in front of a crowd of 23,195.
David Templeton and Francisco Sandaza were both on the bench after lengthy spells on the sidelines through injury, while fit-again youngster Darren Cole was also among the substitutes for the first time this season.
The match was less than two minutes old when Rangers had the ball in the back of the net through Kyle.
But he was denied the opener by the offside flag and the decision looked like it may have been harsh on the striker.
A minute of applause rang around the stadium in the 2nd minute in support of Light Blues legend Sandy Jardine who is being treated for cancer.
Rangers continued to threaten and the lively Barrie McKay surged into the box from the left before teeing up the shot for Kyle but he connected awkwardly in front of goal and the chance was lost.
At the other end, Neil Alexander was called into action to block an angled drive from Craig Gunn.
The home side still looked the more likely to find the back of the net and Shiels stung the palms of goalkeeper John Gibson with a powerful shot.
Gibson was called into action again moments later, this time to tip wide an impressive 30-yard effort from Ian Black.
With half-time approaching and the match still deadlocked, Lee Wallace burst past Jamie Duff down the left flank before cutting back for Kyle but he fired wide.
Shiels finally had the net bulging two minutes before the break with a shot from a tight angle that fell across the goalkeeper and nestled in the far bottom corner.
Elgin were not too far away shortly after the re-start when Stuart Leslie rifled into the side netting after collecting a teasing ball across the face of goal.
Kyle then squandered the chance to double Rangers' lead when he met a McKay cross only to see his header flash wide of the upright.
Black had required treatment for a knock earlier in the game and, clearly still struggling, was replaced by Cole on the hour-mark.
Cole immediately set up Andy Little for a diving header that was off target, before Shiels was prevented from claiming his second of the day by an impressive block from Gibson.
But the goalkeeper was picking the ball out of the net after 69 minutes when Kyle rose above everyone in the box to connect with a McKay corner and nod past the grasp of Gibson.
Only a great save from Alexander prevented Sean Crighton from pulling a goal back for Elgin, before Templeton was thrown into the action with just under 20 minutes to go.
McKay was denied by the woodwork when his deflected effort crashed off the post, before substitute Naismith put the gloss on the win when he slotted past Gibson with 85 minutes on the clock, seconds after replacing Kyle.
- Sports & Recreation