The most taxing aspect of this Ramsdens Cup tie for Rangers was making sense of the eligibility rules.

Ally McCoist could select two of his new players as trialists, and only then from those who are already registered in Scotland because they played in the country last season. The game itself was a straightforward assignment, although that represents a form of progress for a team that struggled on occasion against lesser opponents last year.

The assumption is that Rangers will comfortably win SPFL League One, so cup ties are an opportunity to emphasise that the club have not allowed their ambitions to diminish during a spell in the lower leagues. This competition will have the lowest priority, but it must have been pleasing for Ally McCoist to see two of his arrivals make an immediate impact. Nicky Law, in particular, was eye-catching as he scored two goals with quality finishes and brought some aplomb to the midfield.

"It was the perfect debut," said Law. "You want to play well and the goals were an added bonus – I just hope they don't expect that from me every week. I got six and seven for Motherwell and that was okay. But at Rangers I should probably get more chances, so I'd like double figures."

Albion Rovers were obliging opponents, since the extent of their ambition appeared to be restricting the visitors from Glasgow. No greater intent could be expected as James Ward was taking charge of the side in his first competitive game as a manager. His main task is to revive a club that was relegated to League Two, so this must have felt like an early nuisance. "We'll be glad to get back to normality and concentrate on what's ahead of us," said Ward.

Complications had to be worked out right up until kick-off. McCoist could not have foreseen the injury to Emilson Cribari's groin during the warm-up, and Kyle McAusland was moved from the substitutes bench to the starting line-up. Problems will always arise, and one of the motivations behind Rangers' recruitment policy this summer has been adding strength in depth to the squad.

The sight of David Templeton coming off the bench in the second half and lashing an assured shot beyond Neil Parry from long range to complete the scoring was further justification of the approach.

None the less, continuity can still be a benefit. Although Scott Gallacher is the second-choice goalkeeper, he has come through the ranks at Ibrox, so was a familiar figure to his defenders. He could ease himself in to his first competitive start for the club, with Albion Rovers taking 71 minutes to properly trouble him. Even then, Gallacher dealt with Mark McGuigan's shot comfortably.

The first competitive game of the season does not always go to plan, but there were at least no hindrances to this campaign for Rangers. The players enjoyed a full pre-season regime, unlike last year, and were therefore obliged to be immediately decisive.

Daly and Law did not feel this was a burden. They are both accomplished enough to have played prominent roles in the Scottish top flight, and Rangers were evidently improved by their presence. Daly's best interventions tended to be with his head or his chest, and Rangers were able to construct moves around the nous of his touch and positioning.

Law was more refined, and the attacking thrust of his play was a dimension the team lacked last season. Lewis Macleod was not inhibited by the appearance of a rival for a place in midfield, responding instead by reminding that he can be a slick, inventive player himself. He was alert enough to recognise the opportunity as Lee Wallace surged forward on the overlap and his pass allowed the full-back to measure his delivery into the penalty area, where Law comfortably side-footed a shot high into the net for the opening goal.

Rangers had taken control of the game by stealth. They did not overwhelm Albion Rovers, but a general efficiency was enough. There were still idiosyncrasies, and Ian Black managed to lift a shot over the stand from close range. The midfielder was more accurate after the break, when he drilled a low shot beneath Parry after Daly sent him through. Generally, Rangers were in command.

Resistance was mostly futile anyway. From Wallace's short corner, Law stepped away from a meek challenge and curled a shot beyond Parry into the far corner of the net. Coming just before half-time, the goal all but confirmed the outcome since Albion Rovers had shown little likelihood of breaking beyond the Rangers defence.

"We were set up to be organised and play our way into it," said Ward. "We were getting to that point but unfortunately a decision didn't go our way, which was the handball at the start of the move which led to the first goal. The referee told me it was accidental. Then the goal before half-time killed us."