The England all-rounder smashed 85 not out off 46 balls as the Rapids reached their challenging 185 target with eight balls to spare.
Moeen was given excellent support by Riki Wessels who finished unbeaten on 65 off 51 balls.
The pair shared in an unbroken stand of 138 – a record for any wicket by either side in T20 matches between the two counties.
The Bears opted to bat and Sam Hain collected four boundaries in the first three overs from Dillon Pennington and Wayne Parnell.
But the last ball of the powerplay accounted for Dominic Sibley (14) who tried to sweep Ed Barnard and Ben Cox completed a stumping.
Hain (46) – after adding 53 with Adam Hose – holed out to Barnard at deep mid-wicket off Pennington.
Hose (48 off 23 balls) brought the 100 up in the 13th over with a six off Barnard over long off but in the same over was caught at cover.
Moeen bowled Will Rhodes (1) but some lusty hitting by Matt Lamb and Michael Burgess (28 not out) added 63 in six overs before Lamb (35 off 22 balls) tried a scoop shot against Parnell and only picked out keeper Cox.
Wessels and Martin Guptill laid the foundations for the Rapids reply by bringing up the 50 in 5.1 overs.
But the Black Caps batsman, after making 27 off 16 balls, was well caught at cover off the next delivery from the spinner.
Moeen was soon into his stride with a six and four off successive balls from Brookes and three boundaries in the next over from Thomson.
The Rapids were well placed at 97-1 after 10 overs and then Moeen smashed the first two deliveries from Will Rhodes for six and reached a 28 ball 50 with a leg glance for four in the same over which cost 19 runs.
Wessels completed a responsible half century in a supporting role off 42 balls and the 100 stand came up in 10 overs.
Moeen then smote successive sixes off Thomson over long on to effectively seal victory for his side.