Nearly 40,000 fans packed Ibrox as Rangers made their home debut as a Third Division club by easing aside East Fife in the Scottish League Cup.
Kick-off was delayed for 20 minutes, but it only took another 15 for Lee McCulloch to roll in the opening goal.
It was set up by Dean Shiels, the new signing lofted in the second after 34 minutes and Lee Wallace hammered the third home a minute after the break.
McCulloch fired in after 62 minutes as Rangers cruised into the second round.
Rangers had made four signings this week, but strikers Kevin Kyle and Francisco Sandaza could only make the bench after being introduced to a crowd that was still pouring into Ibrox after the official kick-off time.
Brazilian defender Emilson Cribari was unable to feature as he is still awaiting international clearance and the same problem denied Trinidad and Tobago forward Collin Samuel the chance to face Rangers again following his previous spells with Falkirk, Dundee United and St Johnstone.
Samuel's latest club might have been the seeded team courtesy of their Second Division status, but they were clear underdogs as Ibrox rocked in defiance at the decision to deny their club a place in the Scottish Premier League.
Yet the visitors' David Muir squandered an early chance before the side who will begin their Division Three campaign at the weekend launched wave after wave of attack.
Goalkeeper Michael Brown superbly turned a glancing header from Andy Little round the post and McCulloch headed over.
Those chances came from debutant Shiels' corners and it was the former Kilmarnock man who played McCulloch in for the opening goal.
Shiels and Dorin Goian both went close before the former lifted the ball over Brown to increase the lead after being set up by teenage midfielder Lewis MacLeod.
Gareth Wardlaw had a good chance to pull a goal back shortly before the break, but the former St Mirren and Ayr United striker was leaning back and fired over.
The traffic was back towards the East Fife goal after half time and, when Brown parried a powerful drive from Shiels, Wallace made no mistake with the rebound.
Teenage winger Barry McKay turned provider for McCulloch's second with Ibrox in party mood.
Robert Sloan finally forced Rangers goalkeeper Neil Alexander into a save with a curling free-kick before Sandaza and Kyle made their Rangers debuts as substitutes.
The Fifers denied either a debut goal, but it was Rangers who moved into Thursday's second-round draw, when several SPL sides will be hoping to avoid the unseeded Ibrox outfit.
New East Fife manager Gordon Durie, the former Rangers striker, will have to be content with a bumper pay day from the shared attendance that looked more than the official figure of 38,000.
Rangers manager Ally McCoist : "We have signed, in my opinion, real quality - possibly Kilmarnock's best player last year in Dean Shiels and possibly Hearts best player last year in Ian Black.
"We've got Kevin Kyle and Sandaza, who will be a handful to any defence.
"But we still need to bring more players in.
"I would like another home tie. That crowd tonight was incredible."
East Fife manager Gordon Durie : "Disappointed at the result but delighted at the attitude of my players.
"They can go home with their heads held high.
They are not going to come up against that quality week-in, week-out.
"They can only learn playing against quality like that and, if you make mistakes against a team of that quality, they will punish you."
Teams: Rangers: Alexander, Goian, Bocanegra, Broadfoot, Wallace, McCulloch, Black (Hutton 81), Shiels, MacLeod (Sandaza 67), Little, McKay (Kyle 81).
Goals: McCullogh 15, 62, Shiels 34, Wallace 46.
Substitutes not used: Gallacher, Christopher Hegarty.
East Fife: Brown, Durie, Cook, Campbell, McCormack, Johnstone (Brown 81), Muir, Smith, McQuade (Jamieson 61), Wardlaw, McBride (Sloan 61).
Substitutes: Collier, White.
Ref: McKendrick. Att: 38,160.