Lee McCulloch claimed a double and Lee Wallace was also on the scoresheet in the first match at Ibrox since Rangers were consigned to liquidation and voted into the Irn-Bru Third Division.
This game was always likely to attract a bigger than usual crowd for a cup tie on a Tuesday night, with an official attendance of 38,160.
But the demand for tickets was so great ahead of kick-off, the start time was delayed by 15 minutes with a large number of fans still outside at 7.45pm.
Inside the stadium, Rangers legend Sandy Jardine addressed the crowd and thanked them for their support during one of the darkest periods in the club’s history.
Shiels was handed his debut from the start, following his arrival last week, while Kevin Kyle and Francisco Sandaza – who both signed earlier today – were named on the bench.
The third of today’s new recruits, Brazilian Emilson Cribari, was unable to feature in the first round tie as he is still awaiting international clearance.
The first real chance fell to Andy Little, whose bullet header forced an excellent reflex save from goalkeeper Michael Brown.
The breakthrough came after 15 minutes when McCulloch, who grabbed an extra-time winner in the Ramsdens Cup against Brechin, raced on to a lovely pass from Shiels and slotted past the helpless Brown.
Shiels then fired inches past the upright and defender Dorin Goian was not too far away with an overhead kick that the Fifers keeper just managed to tip over the crossbar.
The visitors, who had brought a decent travelling support of their own, were dealt a further blow when Shiels doubled the lead after 33 minutes and opened his Rangers account.
Youngster Barrie McKay’s shot was blocked by Brown and former Kilmarnock midfielder Shiels pounced on the loose ball and dinked over the goalkeeper and into the back of the net.
McCulloch could have claimed his second of the night when he met a Wallace cut-back six yards from goal but Brown somehow managed to save with his out-stretched foot.
East Fife had struggled to cause any real problems in front of goal but Gareth Wardlaw could have pulled a goal back just before the break only to blast over instead.
Former Ibrox striker Gordon Durie’s Second Division side were simply no match for Rangers and the tie was over as a contest two minutes after the restart.
McKay embarked on an impressive run before teeing up the shot for Shiels and, again, Brown did well to block but the rebound fell for Wallace and he drove low into the back of the net.
Rangers’ fourth of the night came after 62 minutes when McKay turned provider for McCulloch with a through ball past the defence and the veteran utility man fired home for his brace.
With no way back for the visitors, Sandaza made his bow when he was thrown into the action with just over 20 minutes to go, before Kyle was given the last 10 minutes.