Zimbabwe needed a bowl-off to beat Canada after the two sides tied in their quadrangular series game in King City.
Zimbabwe took it 3-1 after Harvir Baidwan, Sunil Dhaniram and Abdool Samad all missed for Canada, sparing the Africans' blushes.
But the hosts really should have won the game before that drama, as Zimbabwe needed a misfield from Dean Abzal on the boundary to level with Canada's total of 135 for seven.
Zimbabwe was comfortable in its chase until Rizwan Cheema took two wickets in an over to leave them struggling on 34 for three, which became 61 for five.
Wicketkeeper Tatenda Taibu and Elton Chigumbura then staged a 53-run partnership.
But Uganda-born seamer Henry Osinde removed Chigumbura (30 off 19 balls) and held catches in the deep to remove Timycen Maruma and Taibu (37 off 40) from the first two balls of the final over, bowled by Baidwan.
Azbal misfielded with Zimbabwe needing six to win off two balls and Prosper Utseya scrambled a leg bye off the final ball to ensure they finished level with one wicket remaining.
Earlier, Canada's innings had got off to a terrible start when Chigumbura bowled wicketkeeper Ashif Mulla with the first ball of the game, and the hosts lost regular wickets thereafter.
Four Canada batsmen, Cheema, Mohammad Iqbal, Karun Jethi and Balaji Rao, passed 20, but none could go on.
Utseya's off-spin proved particularly effective as the Zimbabwe captain returned figures of one for 12 off his four overs.
Canada v Zimbabwe
Canada innings
Mulla b Chigumbura 0 (1)
Cheema c Taibu Chigumbura 23 (11)
Mohammad Iqbal b Price 22 (25)
Samad run out (Mupariwa) 18 (11)
David c Maruma b Utseya 2 (11)
Dhaniram run out (Chigumbura) 5 (14)
Jethi st Taibu b Maruma 24 (24)
Balaji Rao not out 22 (15)
Bhatti not out 4 (8)
Extras 15 (b 4, lb 7, w 4)
Total 135 (7 wickets; 20 overs)
FoW: 1-0 (Mulla, 0.1 ov), 2-32 (Rizwan Cheema, 2.4 ov), 3-59 (Samad, 5.5 ov), 4-71 (David, 9.3 ov), 5-71 (Mohammad Iqbal, 10.2 ov), 6-78 (Dhaniram, 13.4 ov), 7-108 (Jethi, 17.2 ov)
Bowling
Chigumbura 3-0-31-2 (1w)
Mupawira 4-0-31-0 (3w)
Price 4-1-17-1
Utseya 4-0-12-1
Dabengwa 3-0-25-0
Maruma 2-0-8-1
Zimbabwe innings
Masakadza c David b Rizwan Cheema 15 (11)
Zhuwawo c Baidwan b Osinde 0 (1)
Chiobhabha c Baidwan b Rizwan Cheema 17 (23)
Taibu c Osinde b Baidwan 37 (38)
Matsikenyeri lbw b Baidwan 6 (7)
Dabengwa c Mulla b Balaji Rao 6 (8)
Chigumbura b Osinde 30 (20)
Maruma c Osinde b Baidwan 4 (8)
Mupariwa not out 3 (1)
Utseya run out (David) 6 (3)
Extras 11 (b 3, lb 3, w 5)
Total 135 (9 wickets; 20.0 overs)
FoW: 1-1 (Zhuwawo, 0.2 ov), 2-34 (Masakadza, 5.2 ov), 3-34 (Chibhabha, 5.5 ov), 4-51 (Matsikenyeri, 8.6 ov), 5-61 (Dabengwa, 10.6 ov), 6-114 (Chigumbura, 16.5 ov), 7-126 (Maruma, 19.1 ov), 8-126 (Taibu, 19.2 ov), 9-135 (Utseya, 19.6 ov)
Bowling
Osinde 4-0-22-2
Bhatti 2-0-15-0 (1w)
Rizwan Cheema 4-1-19-2 (1w)
Baidwan 4-0-27-3 (1w)
Dhaniram 3-0-22-0
Balaji Rao 3-0-24-1
Zimbabwe win in bowl off 3-1
Player of the Match Taibu