Ian Black and David Templeton also contributed to the goal haul in the first-round tie against the Scottish League 2 side.
This proved to be a far more convincing and professional start to the season for Rangers than this time last year when they needed extra-time to see off Brechin days after finding themselves dumped in Scottish football's bottom tier.
Law and Jon Daly both made their competitive debuts as trialists against Rovers, with a transfer embargo meaning the Light Blues were only able to name two of their new signings as trialists for this tie.
Further restrictions meant only those who played their football in Scotland last season were eligible for selection as trialists.
Other new recruits, who were registered with foreign associations last term, have to wait until September 1 when Rangers' transfer embargo is lifted.
A late change to the team-sheet saw Kyle McAusland replace Emilson Cribari and make his first senior team start, while reserve goalkeeper Scott Gallacher made his competitive bow for the first team between the sticks.
On a day of debuts, Albion Rovers boss James Ward was in the dug-out for the first time for the clash at neutral Almondvale, which was selected instead of tiny Cliftonhill for the televised tie.
Rangers dominated the possession early on and had the chance to pile on the pressure when Andy Little won a free-kick just outside the box but Law failed to clear the Albion wall with his effort.
Little then met a Lee Wallace cross with a header that lacked purchase and was comfortably claimed by goalkeeper Neil Parry.
The pressure paid off and Rangers were ahead with 26 minutes on the clock.
The move began when Lewis Macleod released Wallace down the left flank and he delivered a teasing ball into the box where Law was waiting to lash home.
The former Motherwell man was celebrating again two minutes before the break when he collected a short corner from Wallace and sent a lovely curling effort beyond the grasp of Parry and into the far top corner.
Templeton was thrown into the action in place of Macleod after 66 minutes, having recovered from the injury that hampered his pre-season preparations.
The tie was beyond Rovers four minutes later when Black met a neat ball from Daly and dispatched an angled drive into the net.
Templeton then added his name to the scoresheet with an unstoppable, ferocious 30-yard drive that left Parry with no chance.
- Sports & Recreation
- David Templeton
- Albion Rovers