"We managed to pick wickets at regular intervals. It was important for us to get the bonus point, but it was not to be. I am pretty happy with the win."
New Zealand, who beat India by 200 runs in the opening match on Tuesday, tasted early success when fast bowler Kyle Mills removed Tillakaratne Dilshan in his second over.
Sangakkara and Tharanga steadied the innings with an 85-run stand for the second wicket. The Sri Lankan captain made 48 before falling to a superb catch by Martin Guptill in the covers off seamer Scott Styris.
Tharanga, dropped on 44 by Styris in the slips off spinner Nathan McCullum, was caught in the deep by debutant Bradley-John Watling off Mills, but not before putting his team in a strong position.
Thilan Samaraweera (36 not out) completed the win when he hit a four off Mills, who was the most successful bowler with 4-41.
"We were outplayed. A total of 190 could have been enough if we had taken wickets. That didn't happen," New Zealand skipper Ross Taylor said.
"We picked up three-four wickets towards the end which made it appear a lot closer than it really was. Watling played really well. It's not easy when you are facing Malinga for the first time."
Sri Lanka earlier did not allow New Zealand to build a big partnership, the highest stand being of 52 runs for the fourth wicket between opener Watling (55) and all-rounder Styris (24). McCullum contributed 36.
Malinga struck with the second delivery of the match when he had Guptill caught by Chamara Kapugedara for his 100th victim in one-day internationals.
Watling and Taylor (16) then put on 45 for the third wicket before Mathews bagged two wickets off three balls.
Mathews trapped the New Zealand captain leg-before and then had Kane Williamson caught by Samaraweera in the slips.
Watling, 25, completed his half-century in style when he hit left-arm spinner Rangana Herath for a four.
He fell soon, top-edging a pull off Mathews to be caught by wicket-keeper Sangakkara. He struck eight fours in his 68-ball knock.
Malinga grabbed two wickets off successive balls in his second spell, dismissing Gareth Hopkins (11) and Daryl Tuffey for no score.