Miller, now with Turkish side Bursaspor, gave the Scots an early lead before James McArthur made it 2-0 before the break, with Kris Commons adding a third goal after half-time.
Both sides were hit by injuries and withdrawals but Craig Levein, the Scotland manager, told Sky Sports: "The most pleasing thing was the way they played as a team. "All the effort they put in made the game easier, that was what pleased me the most."
McArthur was a late replacement for Scott Brown, who was injured in the warm-up, and Levein added: "It couldn't have been easy for him. It can't be easy to come in at the last second and stamp your authority on the game but I thought James did it."
Northern Ireland manager Nigel Worthington was heartened ahead of his side's UEFA EURO 2012 qualifiers despite this loss. "We are disappointed with the defeat but I am looking forward to Serbia and Slovenia," Worthington said.
"The plus factor is you have nine, 10 players to come back in who have a wealth of experience to add to the group. Hopefully they will all be fit. Credit to Scotland. They were strong and they were hungry and ran out strong winners."
Miller scored from close range before McArthur's cross found the top corner, with Commons making it 3-0 after a fine pass from Steven Naismith.
The Nations Cup is a four-team tournament also featuring the Republic of Ireland, who beat Wales 3-0 in the inaugural match here on Tuesday. The new tournament is a league format, with all six matches being staged at Lansdowne Road (the rest will take place in May).