After the visitors batted first and made 8-290 in Auckland on Saturday, the home side was bundled out for just 150 in 29.4 overs.
It was a consolation win for Sri Lanka after New Zealand had claimed the first two matches in the three-game series.
The New Zealand batters failed to put on any significant partnerships, with Mark Chapman (81 off 81 balls, with 10 fours and one six) receiving little support.
Mark Chapman top-scored for New Zealand with 81, but he received little support from teammates. (AP PHOTO)
Fernando, who took 3-26 off seven overs, was named man of the match.
His teammates Theekshana (3-35 off 7.4) and Malinga (3-35 off seven) also caused major problems for the Kiwi batters.
Earlier, Pathum Nissanka made 66 in an innings of two parts as Sri Lanka compiled 8-290.
Nissanka reached 50 from 31 balls but almost immediately fell to the ground in pain from an apparent groin or hip strain.
He tried to bat on but was clearly impaired while running between wickets and was 50 not out when he was summoned from the field by Sri Lanka coach Sanith Jayasuriya to receive medical treatment.
Nissanka returned when Sri Lanka were 4-183 in the 34th over, after Kamindu Mendis was out for 46. He hit two fours and a six, adding 16 runs to his total before he was out in the 37th over when Sri Lanka were 5-204.
Sri Lanka's top order finally fired on Saturday after having failed to do so in the first two matches, which New Zealand won by nine wickets and 113 runs to take an unassailable 2-0 lead in the series.
After Nissanka's dimissal, Janith Liyanaga made a half-century from 51 balls with three fours and two sixes and was out for 53 as Sri Lanka added 76 runs from the last 10 overs.
Matt Henry proved damaging with the ball, taking 4-55 for New Zealand.
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