Kane Williamson and Ross Taylor both scored 61 to help the hosts to 294 for five from their 50 overs.
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But Guptill and Kane Williamson (61) put on 122 for the second wicket to put the Kiwis in charge before the latter gloved a catch on the sweep.
Mathews combined with his strong middle order to guide the run chase for 295 to snatch a draw in the series but when he was the eighth wicket to fall for 95, it effectively ended Sri Lanka’s chances and they were bowled out for 258 in 47.1 overs.
Henry, who took four-wicket hauls in two other appearances in the series, finished with 5-40 as Sri Lanka captain Angelo Mathews had threatened to steal victory for his side.
The chasing team have won all three completed games in the series, with New Zealand comprehensive winners twice in Christchurch before Sri Lanka bounced back in Nelson.
Henry bowled Lahiru Thirimanne for two and had Danushka Gunathilaka caught for 15 as Sri Lanka slumped to 33 for 3 after nine overs before Mathews put some respectability into their innings.
The pitch at Bay Oval was dry and hard but its slowness confounded strokemakers in both teams.
But when Siriwardana fell to Mitchell Santner for 39, New Zealand rammed home their advantage.
The milestone comes after innings of 79, 93, 30 and 27 in the previous ODI matches and a century in the first Test against Sri Lanka.
“We kept losing wickets up front and if we had a good start we could have just knocked it around and we could have got to 300”, Mathews said.
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Sri Lanka¿s Angelo Mathews hits a six against New Zealand in the fifth One Day International Cricket match at Blake Park, in Mount Maunganui, Tauranga, New Zealand, Tuesday, Jan. 5, 2016.
