The left-armer then took a vital catch to dismiss Nuwan Kulasekara for 14 in the final over bowled by Grant Elliott, before Chamara Kapugedera was brilliantly run out by Martin Guptill with a bullet throw for 17.
The visitors needed 13 runs off the final over but fell short as Elliott, back after a broken hand, sent down composed six deliveries that kept them off balance and they finished on 179-9 chasing New Zealand's 182-4 in their 20 overs.
Siriwardana and Thisara Perera (28) had got their side back into the game with 49 runs in 32 balls after Boult, Matt Henry and leg spinner Ish Sodhi had reduced the visitors to 84-5 in the 10th over.
The match had been billed by New Zealand coach Mike Hesson as the start of an extended run of selection matches ahead of the World Twenty20 in India with limited overs specialist Colin Munro brought back into the side.
Munro did his chances no harm with the bat, scoring 36 while batting at number three, but his medium pace bowling was too full and did not put pressure on the Sri Lankan batsmen as he conceded 17 runs in two overs.
New Zealand's total had been set up by a century stand by Martin Guptill (58) and Kane Williamson (53), who has taken over the captaincy from Brendon McCullum.
The 34-year-old McCullum was not selected for the Twenty20 matches as he is retiring after next month's series against Australia.
Ross Taylor (22) and Elliott (10) put on 19 in the final 10 balls after Sri Lanka's bowlers had slowed their run rate in the latter part of the innings.
(Reporting by Greg Stutchbury in Wellington; Editing by Amlan Chakraborty)
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