Ross Taylor was on five with debutant Henry Nicholls hitting the winning runs to move to 23 as New Zealand raced to 191 for three in 21 overs.
Captain Brendon McCullum scored 55 from 25 balls in an 108-run opening partnership with Guptill, who moved to 1,366 runs from 30 matches in 2015.
Compatriot Kane Williamson, who has a knee injury and missed the match, has scored 1,317 runs this year, with South Africa's AB de Villiers third on 1,193.
While Guptill and McCullum made light work of the run chase, victory had been set up in Sri Lanka's innings when opening bowlers Adam Milne and Matt Henry reduced the visitors to 27-5 inside the first 10 overs with the latter taking four wickets.
"I thought the wicket was outstanding so for us to take five for 30 up front was a truly outstanding bowling performance," McCullum said in a televised interview.
"I guess that was the winning of the game."
Both Henry and Milne, who started in place of the rested regular new-ball pair of Trent Boult and Tim Southee, were consistently faster than 140 km per hour in their opening spells with the fiery Milne exceeding 150 kph on several deliveries.
The pair also produced a disciplined line and length on a pitch that Sri Lanka captain Angelo Mathews described as "a belter" when he won the toss and elected to bat.
"It was good to have Adam bowling well at the other end and creating pressure," said Henry, who finished with 4-49.
"We are pretty pleased with the way things went and as a bowling group we were fairly happy."
Milinda Siriwardana (66), who was dropped at deep midwicket by Nicholls on 10, and Nuwan Kulasekara (58), however, combined for a 98-run seventh-wicket partnership to give Sri Lanka some credibility.
"We just had to bat and put runs on the board to put pressure on the Kiwis but unfortunately we kept losing wickets in the first 10 overs (and) that was really tough going," said Mathews. "They just bowled well and we couldn't handle it."
The second match is at the same venue on Monday.
(Reporting by Greg Stutchbury in Napier; Editing by John O'Brien)
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