After electing to bat first at the toss, opener Samra struck a brilliant 110 off just 65 balls to to carry Canada to a competitive total of 173-4 in their 20 overs.
It the highest score by an Associate batter against a Full Member in the tournament's history and, at 19 years and 141 days, the left-handed batter also became the youngest to cross fifty in a men's T20 World Cup match.
Samra was part of an opening stand of 116 with his captain Dilpreet Bajwa, who scored 36 but was painstakingly slow as he took 39 balls.
The skipper's laboured knock made sure the Black Caps always had the scoring-rate under control and limited the Canadians to just above the 170-run mark.
The Kiwis were then reduced to 30-2 in pursuit of the target with big-hitting opening pair Tim Seifert (6) and Finn Allen (21) both back in the dressing room inside four overs.
Rachin Ravindra and Glenn Phillips though made sure there no further hiccups as the duo put on an unbeaten partnership of 146 off just 73 balls to take New Zealand to victory with 4.5 overs to spare.
Ravindra finished on 59 not out from 39 balls while Phillips was more destructive for his unbeaten 76 from just 36 deliveries.
The Black Caps finished the group stages with three wins from four matches, with the only defeat coming against South Africa who top the pool.
Zimbabwe have qualified for the Super Eights of the T20 World Cup after their match against Ireland was abandoned without being bowled in Pallekele, with Australia now eliminated from the tournament.
A sensational unbeaten century from Pathum Nissanka powered Sri Lanka to a superb eight-wicket victory over Australia in T20 World Cup action on Monday.
England were made to sweat for large parts but eventually showed their metal before beating Italy by 24 runs to book their place in the next round of the T20 World Cup.
Azmatullah Omarzai starred with bat and ball to help Afghanistan register their first win of their T20 World Cup campaign after beating UAE by five wickets with four balls to spare.
