Rangers could indulge themselves, and the novelty of that feeling ensured that they explored the opportunity fully.

Even the substitutes sought to bring some pomp to their display, and Barrie McKay's two goals in the closing eight minutes were the flourishes of a commanding display. There was a gulf in the two teams' resources, in the home side's favour, but that has not always been reflected in Rangers' results this season.

Opponents have sensed a vulnerability, and Paul Hartley arrived at Ibrox believing his Alloa Athletic side could exploit it to progress in the William Hill Scottish Cup. The notion was not so outlandish, since Queen of the South knocked Rangers out of the Ramsdens Cup, and the goals conceded to Inverness Caledonian Thistle in a 3-0 Scottish Communities League Cup defeat were the result of some abject defending.

Much has been made among supporters of McCoist wearing a tracksuit rather than the traditional suit on the touchline, but he had been uncomfortable with the lacklustre displays and a bold statement must have seemed necessary.

Even in an emphatic performance, his defence could still make him wince, but disorganisation and individual misjudgments can be addressed on the training ground. If it is accepted that this Rangers team remain in the early stages of a work in progress, there was cause for optimism. Ian Black is still a pedestrian figure, and McCoist was furious when the midfielder ambled back into position after conceding a foul while Alloa broke upfield from a quick free-kick, but he was the exception among the middle-to-front players.

Perspective must be applied from the wretchedness of Alloa's display – "The team performance went badly wrong," admitted Hartley – but McCoist dwelled upon the ruthless mood of his side. Dean Shiels' deflected goal after just two minutes allowed the Rangers players to shed any inhibitions, but the passing tempo, the urgent pressing of the ball and the general sense of conviction were already establishing a solid foundation for the home side. It must still perplex the manager that his team are capable of this kind of convincing attitude and approach, yet not always capable of applying it.

Even still, the impressive contributions were plentiful, and Shiels linked deftly with Lee McCulloch in attack. The former has played in several different positions this season, but it was clear that operating in a central role, in the space between the forwards and the midfield, allowed him to grant free rein to his imagination. The two attackers combined for Shiels' second, then for Rangers' third goal. With Lewis MacLeod contributing sure-footed passing and diligence in midfield, and Fraser Aird and Andy Little making incursions down the flank, Rangers were able to play with a rare authority. "The fact that we scored all those goals showed that we can do that," said McKay, who impressed in his late cameo. "It's a good formation to play, especially with the players we've got."

Rangers were adaptable, and losing Anestis Argyriou then Emilson Cribari to injury in the second-half did not disrupt the team's mood. Little dropped to right-back, then McCulloch moved into central defence, and resourcefulness had been evident from the start since Chris Hegarty, a right-sided centre-back, was a reliable left-back.

McCoist could also take heart from the sprightliness of his team in the closing stages – even before Alloa were reduced to 10 men with the dismissal of Michael Doyle for throwing a punch – with McCulloch and Robbie Crawford scoring two goals in the space of a minute before McKay's double. By the end, Rangers had seven players on the field under the age of 23, five of whom were 20 or under, with MacLeod the most assured among them.

"Lewis has played every game, so he's adapted to it well and is playing well," said McKay. "The same with Fraser, he's doing well. It's hard for everybody, the more experienced ones and the younger ones. But [McCoist] talks to you a lot, which is good."