David Dunn's penalty set up a tense finish but Rovers could not capitalise on some late pressure.
Rangers manager Walter Smith fielded Madjid Bougherra at right-back and Andy Webster partnered David Weir in central defence. Steven Davis was given a central role in a five-man midfield with Kyle Lafferty and Steven Naismith out wide to support Miller up front.
Rovers had only arrived in Australia 33 hours before kick-off and they made a slow start as Weir, Miller and Lafferty all went close before Edu headed a 10th-minute opener from Davis' free-kick.
Rangers continued to have the better of the play and Naismith and Lafferty combined to set up Miller to blast into the roof of the net from eight yards just before the break.
Rovers improved after the restart and Allan McGregor saved well from Junior Hoilett, but Miller, who has been suffering from shin splints, hit a penalty against the crossbar after Grant Hanley had brought down Edu.
Dunn made no mistake from his spot-kick, which came after Hoilett fell under Bougherra's challenge.
Substitute John Fleck came close for Rangers before Pascal Chimbonda fired over for Sam Allardyce's side in a late flurry.
With each goal worth a point, the win left Rangers on five points, three behind AEK Athens, who opened the tournament with a 5-3 victory over Sydney FC.