Arbroath 0-4 Rangers
Nikica Jelavic returned from injury to inspire Rangers to a comfortable victory over Arbroath in the fourth round of the Scottish Cup.
Rangers goalkeeper Allan McGregor had superbly denied Josh Falkingham before the 17th-minute opener.
Jelavic was involved as Edu set up David Healy to fire past Darren Hill.
Craig Wedderburn deflected a Jelavic cross into his own net, the Croat fired in the third after the break and Salim Kerkar's volley finished the scoring.
A capacity crowd of 5,900 had packed Gayfield Park, with more than half of them praying for the first major shock of the weekend's fourth-round ties.
But the Scottish Premier Leaguechampions clinically inflicted the Second Division promotion hopefuls' first home defeat since their opening fixture of the season, when they were knocked out of the Ramsdens Cup 2-1 by Dundee.
Fit-again top scorer Jelavic returned for Rangers along with John Fleck in place of the injured Kyle Lafferty and suspended Steven Davis.
And the Croatia striker was immediately involved, flicking the ball into the path of Healy, who should have done better than half-volley over from 12 yards.
The Red Lichties, unchanged despite their defeat by Dumbarton, responded without any signs of an inferiority complex and twice came close to taking a surprise lead.
After a slip by Carlos Bocanegra, the United States defender named as captain in Davis's absence, Steven Doris raced into the penalty box and flashed a low drive just wide of the far post from 14 yards.
Falkingham was next to threaten following a corner, his volley deflecting off Maurice Edu and spinning over McGregor, who stretched back to turn the ball over the crossbar.
Healy failed to connect properly when set up by Jelavic 12 yards in front of goal, but Arbroath threatened at a couple more corners before the Northern Ireland striker eventually made the breakthrough.
Jelavic combined with Edu before the USA midfielder slipped the ball through for Healy, who poked the ball under advancing goalkeeper Hill.
The relief was obvious in the Rangers ranks and they stretched their lead five minutes later when a low cross from Jelavic was diverted into his own net by Wedderburn under pressure from Edu.
Arbroath did not let their heads dip and could have been handed a lifeline had Gavin Swankie been awarded a penalty for a jersey tug by Sone Aluko.
The Rangers midfielder survived that scare to force Hill into a good block followed by a fine low save at the other end.
Arbroath player-manager Paul Sheerin had no intention of resorting to a damage-limitation exercise as he swapped a midfielder for a striker at half-time, Liam Caddis being replaced with Lee Sibanda.
However, it was Rangers who squandered a chance immediately after the break, with Fleck diving to send a header well wide following a swift break from Jelavic.
There were muted calls for a penalty when Sibanda bounced off the body of Rangers defender Dorin Goian, but the visitors ended any prospect of a surprise comeback after 58 minutes.
Aluko's clever through ball set up Jelavic and the Croatian finished clinically off the inside of the far post from 12 yards.
Algerian subsitute Kerkar grabbed his first goal for Rangers with a controlled 15-yard volley from a Healy cross 13 minutes from time before missing a chance to stretch the lead further.