The Blue Toon were unable to repeat their upset of two years ago as they went down 3-0 in their League Cup first round tie at Ibrox on Sunday.
Peterhead were shock 2-1 winners when they last visited Ibrox for a Third Division match in 2013.
But this was a totally different Rangers side the Blue Toon were facing and a repeat of that upset was always a big ask.
Rangers were determined to make an impression in their first competitive home match under new boss Mark Warburton and won with goals from David Templeton, Kenny Miller and James Tavernier.
The tone for the afternoon was set when Jamie Stevenson fouled David Templeton on the left and, from the free-kick. Barrie McKay picked out Lee Wallace 12 yards out but Graeme Smith dived to his left to comfortably save his low shot.
Rory McAllister ploughed a lone furrow up front for Peterhead and made some space for himself outside Rangers box but his weak effort trundled wide.
At the other end Smith held a rising Dean Shiels 25-yarder and then kept out another effort from the Rangers player after he had been set up by McKay and Templeton.
McAllister tried a pot shot from 25 yards which was safely held by Wes Foderingham.
But Rangers were soon back on the attack and Tavernier fired a free-kick straight at Smith.
Nicky Law should have opened the scoring for the home side in 24 minutes but his header from Tavernier’s cross flashed inches wide.
Wallace then got beyond the Blue Toon defence only to see Smith stick out a leg to deny him the opener.
Tavernier pounced on a loose ball to send a low sizzler inches wide and Smith was then off his line to save at the feet of Shiels before then safely holding a Halliday drive.
But the Blue Toon finally cracked in 41 minutes,
McKay sent in a low cross which broke to Templeton and Smith was beaten at last as his low shot found the net from eight yards,
Rangers were fortunate not to be reduced to 10 men just before half-time when Halliday appeared to push McAllister in the face with his hand - right in front of Peterhead boss Jim McInally - but neither the referee nor his assistant were inclined to take any action.
Rangers almost doubled their advantage two minutes into the second period when a deflected Martyn Waghorn shot beat Smith but Ryan Strachan was on the line to clear.
Peterhead tried to get up the pitch and won their first corner in 50 minutes but Jamie Stevenson’s kick was easily collected by Wes Foderingham.
The action was soon back at the other end, Waghorn blazing over after latching onto a woefully short Nathan Blockley header.
McKay wasted an opportunity by shooting wide with just Smith to beat and Tavernier fired just wide as Rangers looked to put the game to bed.
But Smith continued to defy them, holding a dipping 25-yarder from the impressive Tavernier.
However the Ibrox side made sure of their place in the second round when they doubled their advantage in the 76th minute.
Once again Tavernier was involved, opening up the left-hand side of Peterhead defence before crossing for substitute KENNY MILLER to steer home at the far post.
Waghorn saw a 20-yard curler crash off a post before Rangers went three up in 82 minutes, Andy Halliday breaking through the middle before setting up TAVERNIER to fire low past the helpless Smith.
Striker Waghorn blazed over from 18 yards and Smith made further stunning saves to keep out efforts from Jason Holt and Waghorn as Rangers threatened to inflict further punishment on a tiring Blue Toon.
But in the end there was no further scoring.
Peterhead: Smith, Blockley, Noble, Strachan, Ross, Dzierzawski, Stevenson (McIntosh 53), Redman, McAllister, Sutherland, Brown. Subs: Jarvie, McIntosh, Rogers, Ferris, Adams, Lawrence, Baptie.
Rangers: Foderingham, Tavernier, Kiernan, Wallace, Law, Templeton, Halliday, McKay (Clark 71), Shiels, Wilson, Waghorn. Subs: Kelly, Aird, Zaliukas, Walsh.
Referee: Greg Aitken.
Peterhead: Smith, Blockley, Noble, Strachan, Ross, Dzierzawski, Stevenson, Redman (Rogers 75), McAllister, Sutherland, Brown (Ferris 66). Subs: Jarvie, Adams, Lawrence, Baptie.
Rangers: Foderingham, Tavernier, Kiernan, Wallace, Law (Holt 58), Templeton (Miller 58), Halliday, McKay, Shiels, Wilson, Waghorn. Subs: Kelly, Miller, Clark, Aird, Holt, Zaliukas, Walsh.
Referee: Greg Aitken.