Vincent's 101 was the centrepiece of New Zealand's World Cup record score of 363 for five.
The innings also saw Brendon McCullum (52 not out) score the fastest World Cup 50 of all-time, off 20 balls with five sixes and one four, as Canada's attack wilted.
Canada captain John Davison, who four years ago scored the fastest World Cup hundred, off 67 balls, counter-attacked by making 52 before he was caught and bowled by paceman Michael Mason.
New Zealand's total was also a Beausejour ground record in one-day internationals, coming just two days after they'd posted the previous best here of 331 for seven against Kenya.
Davison went on the offensive against an attack missing rested fast bowler Shane Bond.
Off the fifth ball, from Daryl Tuffey, playing his first match of the tournament, Davison pulled a six and he later weighed in with four succesive fours off Mason.
Left-hander Geoff Barnett then got in on the act with four off Tuffey.
By then Davison had been bowled off a Mason no-ball and there was further frustration for the Black Caps when Barnett, on 15, was dropped by a diving McCullum off Tuffey.
Canada's 50 came in just 30 balls before, with the score on 76, they lost their first wicket.
Going for another boundary to add to his six and 10 fours, Davison miscued the ball straight up in their air and Mason made no mistake.
Davison had faced a mere 31 balls.
The run-rate slowed and McCullum made amends for his earlier error by holding an edged cut from Barnett (40) off left-arm spinner Daniel Vettori to leave Canada 110 for two.
Ian Billcliff, who has played for several New Zealand first-class sides, made 50 off 55 balls with four four fours.
But one ball later he was bowled by medium-pacer Scott Styris and from their Canada's innings fell away.
However, their total of 249 for was their best at the World Cup, surpassing the 228 for seven they made in Sunday's 51-run defeat by England and once more they took the game to the last over.
This was a 'dead' match, with New Zealand already through to the Super Eights and Canada unable to qualify for the second phase after losing to Kenya and England.
Vincent, after Davison won the toss, struggled early on against some fine outswing bowling from former West Indies fast bowler Anderson Cummins.
However, he got off the mark in fine style at the start of the third over when he lofted Cummins for six over extra-cover.
Both Vincent and New Zealand captain Stephen Fleming, who made 66, opened up before a stand worth 142 ended when Fleming chipped left-arm spinner Kevin Sandher, making his World Cup debut, to Ian Billcliff at mid-wicket Vincent's single off Sunil Dhaniram took him to a hundred off 115 balls with one six and nine fours.
But two balls later Vincent chipped a return catch to off-spinner Davison. McCullum, however, made sure the runs kept coming by lofting Sandher onto the roof of the stand at mid-wicket while Jacob Oram (35 not out) drove Cummins's last ball down the ground for six.
Both batsmen cleared the boundary with ease as 22 runs came off the last over from Sunil Dhaniram, the left-arm spinner conceding an expensive 72 in eight overs.