Upul Tharanga and Tillakaratne Dilshan shared 63 and Jayawardene put on 179 in 137 balls with Kumar Sangakkara (92).
Jayawardene reached three figures from 80 balls and hit nine fours and a six as the Sri Lankans amassed 332-7.
Canada lost John Davison first ball in the second over and were 122 all out, paceman Nuwan Kulasekera taking 3-16.
Jayawardene's masterful 13th one-day international century was the fourth-fastest in World Cup history and underlined why the Sri Lankans are amongst the favourites to regain the title they won so magnificently in 1996.
Their openers did not make the explosive start expected, however, after Sangakkara chose to bat at the new Mahinda Rajapaksa International Stadium in the rural town of Sooriyawewa in the Southern Province of Sri Lanka, which was hosting its first international match.
On a sweltering afternoon before a capacity crowd of 35,000, the ball did not come on to the bat quite as they would have liked and Dilshan on occasions tried to hit the ball too hard as he struggled to find his timing.
But successive Dilshan boundaries brought up the 50 in the 10th over, before Tharanga ran through for a single only to find his partner still at the bowler's end.
Dilshan passed 5,000 ODI runs and reached his 21st fifty in the 19th over before slashing a wide slower ball from Rizman Cheema to deep point.
Canada were clearly aware of the importance of Jayawardene's wicket and used both their referrals on speculative appeals for catches at the wicket early in his innings, both of which were swiftly rejected.
Jayawardene mastered the wicket at the new venue
The former captain hit the first six of the match in the 25th over when he lofted Jimmy Hansra effortlessly over wide long-on, narrowly missing the motorbike he would later collect as part of his man-of-the-match award.
When Davison tried to bowl wide and flat at him outside the off-stump, he reverse swept for four and when the next one was fizzed in down the leg side it was whipped for four as Jayawardene reached 50 from 40 balls.
It also inspired Sangakkara, who was dropped on 12 by 16-year-old substitute fielder Nitish Kumar, diving for a tough chance in the gully.
Sangakkara skipped down the wicket to launch Balaji Rao straight down the ground for six and pulled a full toss from Harvir Baidwan dismissively for four to record both his 60th ODI fifty and the 100 partnership from 82 balls.
Sri Lanka's fourth fifty came from a mere 34 balls and with their illustrious partnership firing at 10 runs per over, the only surprise was when Sangakkara drove a return catch off the bottom of the bat straight to Davison.
Jayawardene's only concern was cramp caused by the extreme heat and off the next ball he received after completing his century he was caught at short fine-leg from the final delivery of the 44th over.
Sangakkara could conceivably have declared at that point but Thilan Samaraweera helped his team to their second-highest World Cup total.
Sri Lanka bowled out Canada for 36 in the 2003 World Cup and even though Lasith Malinga was resting a sore back, with Kulasekara and Thisara Perera finding swing and seam movement at pace under the floodlights it looked as though that might come under threat.
Davison hit the then-fastest World Cup century against West Indies in the 2003 World Cup, which came from 67 deliveries, but the 40-year-old was beaten for pace by Perera as a rapid delivery moved in between bat and pad and rattled the off-bail.
Perera should have been on a hat-trick when an inswinger was edged by Zubin Surkari next ball but Samaraweera spilled a routine chance at first slip.
It was never likely to prove significant, however, and Ruvindu Gunasekera drove straight to short cover in the next over to make it 8-2. Seven balls later, it was 12-3 when Surkari played round one from Perera and was lbw.
Having negotiated five overs without further alarm the Canadians were confronted with the highest wicket-taker in ODI history, Muttiah Muralitharan, in his final competition.
The only doubt for the Sri Lankans was completing 20 overs to constitute a match before the forecasted storms swept in, which may have explained the decision to bowl spin from both ends.
But the rain stayed away and the wickets continued to fall, Perera returning to have Ashish Bagai caught behind for 22 with the third ball of his new spell.
Cheemu hit Murali for two mammoth sixes before scything to backward point after top-scoring with a belligerent 37 from 35 balls and the spinner collected his 521st ODI wicket before spin partner Ajantha Mendis ended the match.
Sangakkara saluted his premier batsman Jayawardene and said: "The openers gave us a solid start but the real star was Mahela Jayawardene; it was very easy to bat with him.
"Once we got that foundation and that solidity, we were able to launch and go beyond 300. Wickets like this when you haven't played before, it's nice to get an idea of what's going on. To see what areas you can score and what bowlers you can score off.
"So I took a bit of time with my innings and then Mahela came in and brought the momentum back."
Canadian skipper Bagai admitted: "It was always going to be a tough task but I thought we bowled well in the first 26 overs where we managed to keep them under five runs an over.
"And then two world class players took the game away from us. So 333 was always going to be a tough ask."
The next match for the Sri Lankas is against Pakistan on Saturday while Canada next play Zimbabwe on 28 February
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