A valiant effort by the Broch was to prove not quite enough to threaten a cup upset as a hattrick by Josh Windass sent Rangers on their travels again, this time to Ayr United.
The home side made it an uncomfortable night for the Glasgow giants but their class in front of goal was to prove decisive.
Bellslea Park was packed to the rafters for this eagerly anticipated Scottish Cup fourth round tie.
Fraserburgh made three changes to their starting line up from the side that had thrashed Forres Mechanics the previous Saturday. Rangers fielded a predictably star studded team containing internationalists and some of their recent signings.
A stiff breeze made an almost immediate impact as a kick out from Jak Alnwick was blown out for a throw in inside the first minute.
The Broch had an early chance, a free kick 25 yards out and slightly to the right of goal but Ryan Cowie sent his shot into the wall with five minutes gone.
It was Rangers who went close after 14 minutes, an incisive pass forward by Nico Kranjcar found Jason Cummings 12 yards out and it took a timely interception to prevent the shot but a minute later the visitors did go in front.
A clumsy challenge by Bryan Hay on Jason Holt to the right of goal saw the referee immediately point to the spot and Josh Windass buried the penalty low into the left corner.
Fraserburgh had loud appeals for a penalty of their own in the 25th minute, Lee Hodson sending Willie West sprawling but the well placed referee would hear none of it.
Almost immediately the visitors could have scored again, a thunderous Kranjcar drive crashing off the crossbar and over.
The Broch made a positive start to the second half earning a corner three minutes in which Lewis Davidson flighted in from the left and West managed the slightest touch with his head but not enough to trouble Alnwick.
The Gers showed their class in fits and starts and after 58 minutes they did just that, the elusive Kranjcar setting up the tricky Windass and at 2 nil the chance of an upset looked well and truly gone.
Midway through the half a Jamie Beagrie turn and shot might have produced thoughts of a comeback but drifted harmlessly wide.
Rangers scored a superb third in the 67th minute, that man Windass gliding parallel to the goal before coolly picking his spot low into the corner for his hat trick.
A Paul Young shot from 18 yards that was always rising kept the home supporters spirits up whilst at the other end Peter Tait pulled out a fine save to deny sub Eduardo Herrera.
The game ended on a sour for Fraserburgh, sub Graham Johnston had been on the pitch all of two minutes when he received a straight red card for a two footed challenge on Joe Doodoo.
Speaking after the match, Fraserburgh manager Mark Cowie said: “It’s a feeling of pride after the game.
“A lot better teams than Fraserburgh have lost by more than three goal to Rangers.
“There are a few debates about the penalty and we started the second half strongly and had them on the back foot for a while.
“They had a huge slice of luck for the second goal when Cummings shot was going wide and landing at the feet of
“Windass but he took the third goal very well and showed his quality and he was the difference.
“Rangers had the vast majority of the ball but we tried to knock the ball around.
“We had a couple of free kicks that we could have done better with but we tired near the end.
“We could have had a penalty but you need the rub of the green.
“We need to get back to the league now after all the hype surrounding the cup tie and keep our aim of a top four finish alive.”