The visitors came to Govan as the Light Blues’ closest challengers and retain two games in hand. A better result might have given them encouragement that the gap at the top could be narrowed for the late part of the season, but it was never in doubt.
The opening half saw Rangers exert the pressure in the early stage and again close to half time without working the Queens keeper until injury time.
Little had a decent early opening after a neat pass from McKay found Hutton in space and he moved it quickly forward to Little.
The Ulsterman had the pace to get to the box but his finish was high and the chance was gone.
Little was clearly keen to impress through the middle and he combined well with Shiels minutes later but still no breakthrough was achieved.
Shiels came a little closer just shy of the twenty minute mark when he struck the side netting from the edge of the box after a good combination with Hutton.
Rangers seemed to be getting closer to the breakthrough but without a goal the visitors started to come in to the game.
With defensive confidence damaged by the previous week’s disappointment at Tannadice it was clear their remained an edginess in front of Neil Alexander.
The keeper was evidently unhappy with the contributions of his defence as Queens threatened to take the lead.
Rangers weathered the brief flurry from the visitors and almost made that count in the closing minutes of the half.
Cribari hit the post with a header from one of the better delivered set pieces, and Rangers were unlucky to see both Shiels and Templeton denied by a fine double save from Neil Parry in first half stoppage time.
The tempo was still there for the start of the second half as Rangers pressured early on and Hutton forced another smart save from Parry.
Shiels followed up on the rebound but his connection was poor and the ball bounced across the face of goal.
The intent would be rewarded within five minutes however, as the home side this time broke down the left through McKay.
He had options with four players pouring in to the box and he picked out the late run of Black who guided a cushioned volley in to the bottom corner.
The move was a sign that McCoist had encouraged Black, and the rest of the midfield, to play further toward the visitors’ goal.
And there was more evidence for the second goal too. McKay on the left was again the out ball and he got things moving.
A brilliant switch of play saw him pick out Templeton who rolled it in to the path of Hutton. The midfielder might have shot, but instead picked out Shiels.
He was equally unselfish to roll the ball in to Little’s path for the simplest of finishes.
That selflessness from Shiels was rewarded when he tucked home the third with a similarly straightforward chance thanks to Wallace’s cutback.
Wallace was again at his consistent best of the left and would have been bemused by the decision of referee George Salmond to ignore Aidan Connolly’s blatant foul on him late in the match.
A second yellow for the midfielder seemed inevitable when he leapt in on the touchline but Salmond opted to allow play to continue.
There remained time for Rangers to add a little gloss, and it was a pleasing end for Andy Little as he added a second and took his season tally to 18.
Rangers: Alexander; Argyriou, Hegarty, Cribari, Wallace; Hutton, Black; McKay (Aird 73), Shiels (Crawford 80), Templeton; Little.
Subs: Gallacher, Faure, Mitchell.
Goals: Black (50), Little (63, 89), Shiels (78)
Bookings: Templeton, Argyriou
Queen’s Park: Parry, Little, Robertson, Keenan (Burns 69), Brough, McPartland, Connolly, Anderson, Longworth, Quinn (Shankland 90), Spittal (Urquhart 59).
Subs: Lochhead, Bradley.
Bookings: Connolly, Robertson, McPartland.
Referee: George Salmond
Attendance: 46,104