Clayton Donaldson made it 2-0 five minutes into the second half. The Rotherham defence couldn't deal with Scott Wiseman's through ball, and Donaldson raced onto it to round the keeper.
Montgomery was then rounded again three minutes later by Strong from another Wiseman set up, and the 28-year-old completed his hat-trick with just over an hour gone. Julien Baudet failed to find Montgomery with a header back, and after his first effort was parried, Strong buried the rebound.
City continued to force saves out of Montgomery, but it was the visitors who were next to find the net. Nick Page's right-wing cross was headed down by Andy Monkhouse, and Andy Jones fired past Paul Musselwhite to pull a goal back.
But sloppy marking from a Dean Keates corner in the final minute allowed Andy Holt to head home and complete a 5-1 victory.
City reserves will be looking to make it three successive wins when they face Bradford in their next match on Wednesday at Church Road, North Ferriby (kick-off: 7pm).
City line-up: Musselwhite; Wiseman, Whittle, Byron, Burton; France, Melton, Keates, Holt; Donaldson, Strong.
Un-used subs: Harvey, Cooper, Tomlinson, Russell, Matthews.