Leverock, who took 5/60 to help skittle the home side for 151, returned with the match figures of 11/72.
It was always going to be an uphill task for Canada on the final day as it started at 32/4 chasing a distant target of 258 and Leverock quickly made the chase an even more unlikely goal with the first three wickets of the day.
First he trapped Ian Billcliff, Canada"s captain and its main hope for success, leg before wicket for 26, then Sunil Dhaniram (22) fell to a Chris Foggo catch and Karun Jethi was stumped by Jekon Edness for four.
Jethi was Leverock"s 10th wicket of the match and Canada was in tatters at 74/7.
To the home side"s credit, it rallied. Arvind Kandappah (29), wicketkeeper Rustam Bhatti (21 not out) and Eoin Katchay (29) all made useful contributions but they were left with far too much to do and off-spinner Rodney Trott (3-28) wrapped up the match with the last three wickets to fall, all of them caught by Stefan Kelly.
Leverock, who also made a vital 29 not out in Bermuda"s second innings to help turn the tide in his side"s favour, was named man of the match.
Bermuda 237 and 248 beat Canada 228 and 151 all out (Kandappah 29, Katchay 29, Ian Bilcliff 26, Dhaniram 22, Bhatti 21 n o; Leverock 5/60, Trott 3/28, Kelly 2/36).