The match was reduced to 36 overs each due to inclement weather and despite a strong performance from Ashish Bagai (60), the Canadians could only make 155/9.
Tamauri Tucker and Irving Romaine both plucked two wickets apiece and left-arm spinner Leverock bowled a tidy spell of 1/17 in eight overs for the visitors, while some excellent fieldwork yielded three run outs.
Bermuda made a slow start in their run chase, but thanks to a solid knock of 60 by man-of-the-match Chris Foggo, they moved to within striking distance of victory.
Jekon Edness guided the tourists home with 18 runs off just 14 balls, as Bermuda reached 158/7 with just three balls to spare.
Qaiser Ali had a good day with the ball to finish with the impressive figures of 3/28 while Dhaniram returned with 2/22.
Canada 155/9 in 36 overs (Ashish Bagai 60, Abdur Samad 26; Romaine 2/32, Tucker 2/25, Leverock 1/17) lost to Bermuda 158/7 in 35.3 overs (Foggo 60, Romaine 21, Edness 18 n o; Qaiser Ali 3/28, Dhaniram 2/22).