The home side missed a plethora of chances throughout the 90 minutes, but strikes from David Templeton and Kenny Miller ensured safe passage to tomorrow afternoon’s draw at Hampden.
Manager Mark Warburton made one change to his starting line-up, with Dean Shiels replacing Jason Holt following last week’s 6-2 defeat of Hibernian.
A little over 25,000 supporters turned-out at Ibrox, and they were treated to a display of high-class passing football from Warburton’s boys, although at times a little cutting-edge was absent from the home side’s game.
James Tavernier marked his debut last week with a stunning free-kick, and he attempted to better that strike early-on with a 30-yard dipping effort that sailed just over the bar.
Lee Wallace then came close when he tried to side-foot a Barrie McKay free-kick through traffic and into the back of the net from the edge of the area, but former ‘Gers goalkeeper Graeme Smith was alert to the danger and gathered with ease.
Dean Shiels looked lively in the opening stages on his return to the XI, and he was next to test Smith with a 25 yard drive that was headed for the top corner, although it lacked the power to properly trouble the stopper.
Shiels again came close when he was slipped-in by McKay, but Scott Ross managed to deflect his effort in to the grateful gloves of Smith.
Peterhead rarely threatened, and their best opportunity of the opening quarter came through Jordon Brown who ran towards goal before unloading his shot 25-yards or so from the target, but his effort was well over and failed to bother Wes Foderingham.
Nicky Law almost grabbed an unlikely goal with his head when he met a James Tavernier cross following another quick McKay free-kick, but the effort was well wide of the far post.
Rangers were at times playing some excellent football, and one such move really should have led to the opening goal.
Lee Wallace burst forward in trademark style before finding Martyn Waghorn lurking on the edge of the area. He flicked it to McKay who in turn found Wallace again, but with only Smith to beat, the Rangers captain was denied by the goalkeeper’s legs.
Chances were coming and going at some rate for Gers, and Tavernier came close once more when a failed clearance broke to him to the right of goal before he unleashed a first-time effort that slipped just wide of Smith’s far post.
Shiels then had yet another opportunity when he met a Templeton cross, but Smith managed to turn it behind for a corner before he easily gathered a Halliday effort from the aforementioned kick from the quadrant.
But the pressure eventually told and Rangers took a thoroughly merited lead through David Templeton, and not in keeping with the general play of the Light Blues, it was a somewhat scrappy finish.
Barrie McKay found acres of space out on the left to drive and then cross for Templeton who sclaffed an effort into the bottom right-hand corner beyond the seemingly unbeatable Smith.
The second half began exactly as the first had ended with Rangers immediately flowing forward in search of more goals, and Martyn Waghorn came close to his first Ibrox strike with a drilled effort from the edge of the area that was blocked only by Ryan Strachan of Peterhead on the line.
Waghorn again came close after being played-in by Templeton, but on the volley, he fired over the bar with only Smith to beat, and then Barrie McKay should have scored when he went through one-on-one, but under pressure from the closing Peterhead defence, he shot wide.
Kenny Miller and Jason Holt replaced Law and Templeton after 58 minutes, and Miller had an immediate impact on the game after entering the field.
He raced after Peterhead’s Nathan Blockley who was charging down the right flank, before tackling him, winning the ball and pinging a delicious chip over the Blue Toon defence into the path of Waghorn.
He in turn found the on-rushing Lee Wallace who couldn’t quite sort-out his feet and Smith gathered his effort easily.
The incredible pace Rangers played at which Rangers played was soon to take its toll however, and the game went into something of a lull, with the ratio of chances being created by the home side going down.
A quick Andy Halliday free-kick looked as if it was goalbound before Smith gathered at the last, and then Dean Shiels saw an effort cleared off the line following a neat corner routine involving Waghorn and Miller.
But the game was at long last put to bed with 14 minutes remaining thanks to Kenny Miller.
Tavernier popped-up high on the right once more and he fed a lovely ball along the six-yard box that was missed firstly by Nicky Clark before Miller met it at the back-post and he finished with aplomb.
The goal reinvigorated Rangers, and they upped the tempo significantly to finish the game in sparkling form.
Martyn Waghorn – who had turned-in an excellent shift all afternoon – almost made it three with a tremendous curling effort from the edge of the area that came off the bottom of the upright.
But it was three soon enough thanks to the excellent James Tavernier.
Nicky Clark burst into the box and squared for Tavernier who had come in from the right wing, and he finished beautifully past Smith.
But while Tavernier’s goal had Ibrox on its feet, the full back earned a standing ovation minutes later for a quite wonderful piece of skill where he chased down a loose ball before back-heeling it past the attentions of the Peterhead defender, turning and feeding Waghorn whose shot was over the bar.
Waghorn missed another chance when Smith somehow got his fingers to his shot when he went through on goal , but he too earned a warm round of applause for his considerable efforts.
So 3-0 it finished, but if this is the sort of football Rangers are going to produce this season, the club’s supporters are going to be royally entertained on a weekly basis.
RANGERS: Foderingham; Tavernier, Wilson, Kiernan, Wallace; Shiels, Halliday, Law (Holt, 58); McKay (Clark, 71), Waghorn, Templeton (Miller, 58).
SUBS NOT USED: Kelly, Zaliukas, Aird, Walsh.
PETERHEAD: Smith, Strachan, Ross, Blockley, Noble, Redman, Dzierzawski, Brown (Ferris, 67), Stevenson (McIntosh, 54), McAllister, Sutherland.
SUBS NOT USED: Jarvie, Adams, Lawrence, Baptie.
ATTENDANCE: 25, 608.