Rogers, who was assisted by first innings centurion Sam Robson (41*), put Nottinghamshire's tired bowlers to the sword as they made short work of the 112 required for victory.
The win completes a remarkable turnaround for Middlesex, who lost their first match of the season by an innings against Sussex at Hove.
The first task for Middlesex was to finish off the visitors' second innings, who resumed overnight at 184/5, just 71 runs ahead - though that was a recovery having been just seven runs ahead at one stage with five wickets down.
However, when Notts captain Chris Read edged Tim Murtagh behind for 44 in the second over of the day, the hosts sensed blood. Murtagh ran through the Nottinghamshire tail to finish with figures of 5/61 with only 40 runs being scored by the visiting tail.
Set a target of 112 to win, Rogers and Robson wasted no time, with the total reached after just 18.2 overs.
Australian opener Rogers was aggressive from the off with boundaries all around the ground, finishing with 63 from just 50 balls.
It was a less happy match for Rogers' international team-mate Peter Siddle, on debut for Nottinghamshire, who finished with 0/24, to go with his 0/89 in the first innings.
Middlesex will look to take momentum from this game into their next County Championship match, which is against Yorkshire at Lord's, starting Sunday 27 April.
Highlights: Rogers quick-fire fifty sees Middlesex home