New Zealand battled on day four, with overnight batters Glenn Phillips, and Tom Blundell completing half centuries, before Mitchell Santner struck 67, batting partly in the company of the tail.
But this fight only served to throw into relief their abysmal 88 in the first innings, rather than provide any serious hope of avoiding even an innings defeat.
In the end, having played out 40.4 overs on day four, they lost their final wicket - Santner - still 154 runs behind Sri Lanka.
The hosts had only batted once.
For Sri Lanka, it was their third Test win in a row.
With four matches to go in their World Test Championship cycle, they are now in the hunt for one of those final two spots, though they must hope for other results to go their way too, to have a better chance.
Sri Lanka will be buoyed too by the six-wicket haul achieved by debutant offspinner Nishan Peiris, even if he was expensive as New Zealand's batters went hard at him.
He finished with figures of 9 for 203 in the match, having taken 6 for 170 in the second dig.
Peiris dismissed each of the three half-centurions on day four.
Blundell was out on the third over of the morning, when he missed a reverse sweep (he was trying his second one in a row, having nailed the first for four), and been struck in front of the stumps.
Later, Phillips attempted to launch Peiris over the straight boundary, but found Dimuth Karunaratne at long on.
After lunch, Peiris had Santner stumped when the batter had allowed his back foot to slide out of the crease - the last New Zealand wicket to fall.
In between, Prabath Jayasuriya had bowled both Tim Southee and Ajaz Patel, the latter with a vicious one that leapt back at Ajaz from the rough.
He himself finished with 9 for 181 from the game.
Phillips and Santner were New Zealand's best day four batters, however.
Phillips' main strategy was to get on the back foot as often as possible, and play off the surface.
This frequently worked - allowing him to pounce on even slightly short deliveries, while forcing bowlers to go fuller to him, presenting scoring opportunities down the ground.
He completed his fifty off 66 balls, and would go on to be involved in a 64-run seventh-wicket stand with Santner, to follow the 95-run stand he'd shared with Blundell.
Santner, meanwhile, was not quite as proactive as Phillips, but found the offside productive.
Occasionally, he would dance down the track and look to hit Peiris in particular down the ground.
He collected two sixes and a four this way, and completed his half century soon after lunch, off the 97th ball he faced.
He was out off the third delivery Sri Lanka bowled with their second new ball.
Scores:
Sri Lanka 602 for 5 dec (Kamindu 182, Chandimal 116, Kusal 106*, Mathews 88, Phillips 3-141) beat New Zealand 88 (Jayasuriya 6-42, Peiris 3-33) and 360 (Phillips 78, Santner 67, Conway 61, Blundell 60, Peiris 6-170, Jayasuriya 3-139) by an innings and 154 runs
