The shattered Kenyans then folded, with only Rakep Patel offering resistance with 16 not out as Southee and Jacob Oram finished off the tail to get Kenya all out for 69 in 23.5 overs.
Brendon McCullum was bowled off a free hit but got into his stride and finished off the game with two successive boundaries, as New Zealand reached their target in just eight overs without losing any wicket, to complete a ten-wicket win.
Canada bowled well in the early overs, but did not get a wicket, as openers Upul Tharanga and Tillakaratne Dilshan reached 50 runs.
Both batsmen got the run rate to over 6 and both seemed to be coasting to their centuries, until Sangakkara on 92 gave a simple return catch to John Davison with the score at 267/2.
Captain Ashish Bagai tried to lead a recovery, but once Perera took his wicket to reduce Canada to 53/5, all doubts about the result finished.
Big-hitter Rizwan Cheema took 37, including two huge sixes off spinner Muttiah Muralitharan, but the latter ultimately got his wicket as Canada fell to 122 all out.
The 14th over was hit for 17 runs as the score quickly reached 50, but soon after, Prosper Utseya got Brad Haddin lbw, which was given out of referral.
The Zimbabwean reply was disappointing, as the Australian pace trio of Brett Lee, Shaun Tait and Mitchell Johnson reduced Zimbabwe to 44/4.
Australian captain Ricky Ponting was handed down a Level 1 charge by the ICC, after he damaged a television set in the dressing room following his run-out.
Younis also reached a half-century and fell immediately, before Misbah-ul-Haq and Umar Akmal hit a rapid 118-run partnership, with the latter especially being severe on the bowlers in his 71 off 52 balls.
Both men fell towards the end of the innings as Pakistan reached 317/7, helped quite substantially by the Kenyan bowling which conceded 46 extras.
Kenya started off solidly in their big chase, with openers Morris Ouma and Seren Waters adding 37 for the first wicket until a direct hit from Umar Akmal had the latter run out.
He then ran through the lower middle order and the tail with ease, and ended up with figures of 5/16 from 8 overs as Kenya collapsed to 112 all out, with the only resistance offered by Collins Obuya's 47.
Pakistan captain Shahid Afridi won the toss and decided to bat first against Sri Lanka, one of the pre-tournament favorites.
Misbah stayed not out till the end for a well made 83, but Sri Lanka got the wickets of Umar Akmal and Abdul Razzaq cheaply, and Shahid Afridi before he did too much damage to the score to keep Pakistan to 277/7.
Silva eventually fell for 57 when Kamran did get a stumping right, and despite Nuwan Kulasekara's cameo, Sri Lanka ended up 11 short.
[8] Canadian opening batsman, Nitish Kumar, became the youngest ever player in World Cup cricket, aged 16 years and 283 days.
[11] Martin Guptill and Brendon McCullum set a new record of the highest opening partnership for New Zealand in World Cup matches.