Fast bowler Malinga, the World Cup's joint most successful bowler with 15 wickets, was ruled out of Thursday's Super Eights match after injuring ankle ligaments in practice.
But despite the absence of the 23-year-old, who has made a major impact during the past year with his distinctive, slingy action, Jayawardene's men were still able to restrict New Zealand to 219 for seven.
Left-arm quick Chaminda Vaas, who removed all of the top three on his way to 3-33 and off-spinner Muttiah Muralitharan (three for 32), two of the survivors from Sri Lanka's 1996 World Cup winning team, did the damage.
Vaas's figures also included dismissing New Zealand skipper Stephen Fleming, lbw for nought for the fourth successive time.
Victory was all but assured when another of the 1996 heroes, opening batsman Sanath Jayasuriya (64), shared a century second-wicket stand with Kumar Sangakkara (69 not out).
"We are not a one-man team. We have quality performers like Vaasy and Murali. The last 12 months we've had our injury problems but we've played as a team and that's why we've won matches," said Jayawardene.
"Lasith was probably okay for today but didn't want to take the risk. He bowled a little bit in the morning but the way things are going we just want to make sure he's 100 percent before we let him loose.
"If he's not 100 percent there is a danger he could do his ligaments more and it could be a serious thing."
Jayawardene is also keen to keep Malinga fresh for the last two Super Eights matches against champions Australia here on Monday, and Ireland two days later.
"We'll see what the physio comes up with," said the captain.
"With Lasith not being in the team it gave us a different combination. He's the leading wicket-taker in the tournament.
"That's something we lost but Vaasy put his hand up and performed, Murali did the same, but the other bowlers backed them up," added Jayawardene after his side moved a step nearer the semi-finals by moving into second place, on run-rate, behind Australia.
Modest man-of-the-match Vaas said there was no mystery to his enduring success. "I stick to basics, bowling wicket-to-wicket and in good areas."
Sri Lanka prevented New Zealand spearhead fast bowler Shane Bond taking a wicket, the former policeman restricted to eight overs for 26 runs.
"I thought Sanath and Kumar batted really well. It's always good to have big partnerships when you are chasing," added Jayawardene.
"We batted really well, fielded really well and had a very good game. It was a big one for us."
And he said this win was just what Sri Lanka needed ahead of their match with Australia, bidding for an unprecedented third straight title.
"You don't want to play the best side in the world with a losing mentality. We are looking forward to it."