Martin Guptill top-scored for New Zealand with 102 to give the hosts a competitive, though not daunting, total of 294 for five.
Sri Lanka trails 2-1 – with one match abandoned – and is seeking a victory to square the series.
New Zealand’s Matt Henry reacts after dismissing Sri Lanka’s Chamara Kapugedera for 10 in the fifth One-Day International Cricket match at Blake Park in Mount Maunganui, Tauranga, New Zealand, on Tuesday, January 5, 2016.
His 102, which included nine fours and three sixes off 109 deliveries, elevated him into an elite group with Nathan Astle and Taylor as the only New Zealanders to score 10 or more ODI centuries.
Chasing New Zealand’s 294/5, Sri Lanka lost five wickets in their run chase.
Both Williamson and Taylor made 61.
Sri Lanka’s bowlers did an excellent job at the end of New Zealand’s innings by clamping down on their scoring rate that had threatened to push the score well past 300.
“It was great to improve from the last performance and the way the bowling unit stepped up…we needed to skin the cat another way and they did that very well today off the back of a superb knock from Martin Guptill”, Williamson said.
“The first 10 overs were important for us as they came out hard against us last time and did very well, so it was good to see us learn from that”.
New Zealand have also made one change with Trent Boult replacing Doug Bracewell.
“It was just great to get across the line and take the series win”.
Guptill batted with care and patience, unlike his innings earlier in the series, particularly his memorable 93 off 30 balls in the second game.
The two teams will meet each other again at Bay Oval on Thursday in the first of two Twenty20 matches.