Captain Brendon McCullum struck 65 off 49 balls as the Black Caps put on a rapid 111 for the first wicket.
Kane Williamson added a composed 57 before Corey Anderson blasted 75 off 46 balls to help the hosts to an imposing total of 331-6 from their 50 overs.
In reply, Sri Lanka subsided to 233 all out, with Daniel Vettori taking 2-34.
New Zealand, who play England next, have reached six World Cup semi-finals without ever going on to make the final.
The Black Caps, however, are one of the favourites for this tournament, and this powerful performance against the 2011 finalists underlined why they are so highly-rated.
"We executed our blueprint with the bat," said McCullum. "It was a really good performance all round. We have been waiting a long time for this so it is great to complete our plans."
Put in under grey skies, the hosts immediately attacked the Sri Lanka bowlers with some explosive hitting in the first powerplay.
Williamson recorded his 13th fifty in his last 17 ODIs, before Anderson, playing in his home city, helped New Zealand to add a crucial 102 in the final 10 overs.
Sri Lanka won the World Cup in 1996 and reached the final of the last two tournaments, but they will have to improve on this performance in order to challenge at this tournament.
Influential fast bowler Lasith Malinga was disappointing, conceding 84 runs in 10 wicketless overs.
Sri Lanka's chase began well, with opener Lahiru Thirimanne hitting 65, but was soon derailed by the pace of Trent Boult and the spin of Vettori.
They collapsed from 124-1 to 168-6, with Boult, Adam Milne and Vettori, who reversed his retirement from ODIs last year, capturing two wickets each, and their innings never recovered.
They will hope for a rapid return to form when they face Afghanistan on Saturday.
"They probably scored 30 or 40 runs too many and then we needed someone in our top four to get a hundred," said captain Angelo Matthews.
"But we are not going to panic, we still have five group games left."
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Co-hosts New Zealand got off to a winning start with a resounding 98-run victory over Sri Lanka in the opening match of the World Cup in Christchurch.