While Vince's man-of-the-match performance caught the eye, captain Eoin Morgan was also full of praise for his bowlers, who laid the platform for victory by restricting the Black Caps to 153 for five.
"The game was won and lost in the first innings... James Vince played outstanding well but all credit to the bowlers today," he said.
A three-wicket haul from spinner Mitchell Santner was not enough to rescue the Black Caps, whose batting line-up failed to fire after Morgan won the toss and sent them in.
England's win came despite the absence of several senior players, who have been rested for the series after a gruelling period that saw them win the World Cup and fail to reclaim the Ashes.
A trio of debutants in the team facing New Zealand fitted in seamlessly, with Sam Curran and Pat Brown both snaring a wicket each. All-rounder Lewis Gregory was not needed with either bat or ball and will hope to make an impression when hostilities resume in Wellington on Sunday.
Morgan said his squad was building its depth by blooding youngsters ahead of the T20 World Cup in Australia next year. "It's a chance for them to stake their claim," said the England captain, who emphatically ended the match with a six off the final ball to finish on 34 not out.
New Zealand's regular captain Kane Williamson is out of the series with a hip injury and the Black Caps sorely missed his batting prowess.
Stand-in skipper Tim Southee said there was room for improvement in bowling, batting and fielding.
"We were probably a little bit off in all three areas," he said.
"We got a score on the board that we felt we could defend but we were a little bit off with the ball and in the field, which didn't help."
The poor form that dogged Martin Guptill at the World Cup continued when Curran coaxed an inside edge that crashed into middle stump.
Fellow opener Colin Munro tried to break the shackles but was too aggressive against Chris Jordan and was caught on the boundary for 21.-AFP
Scoreboard
====================================================== New Zealand ====================================================== M. Guptill b S.Curran 2 C. Munro c Morgan b Jordan 21 T. Siefert c Bairstow b Jordan 32 C. de Grandhomme c Vince b Rashid 19 R. Taylor c Bairstow b Brown 44 D. Mitchell not out 30 M.Santner not out 1 Extras: (lb3, w1) 4 ====================================================== Total: (5 wkts, 20 overs) 153 ======================================================
Fall of wickets: 1-6 (Guptill), 2-39 (Munro), 3-72 (de Grandhomme), 4-93 (Siefert), 5-149 (Taylor)
Bowling: S.Curran 4-0-33-1, T.Curran 4-1-25-0 (xw), Jordan 4-0-28-2, Rashid 4-0-31-1, Brown 4-0-33-1
======================================================
England:
======================================================
J. Bairstow c Guptill b Santner 35
D. Malan c Sodhi b Santner 11
J. Vince c Guptill b Santner 59
E. Morgan not out 34
S. Billings not out 14
Extras (w1) 1
======================================================
Total: (3 wkts, 18.3 overs) 154
======================================================
Fall of wickets: 1-37 (Malan), 2-68 (Bairstow), 3-122 (Vince) Bowling: Southee 3.3-0-30-0 (1w), Ferguson 4-0-28-8, Kuggeleijn 3-0-35-0, Santner 4-0-23-3, Sodhi 4-0-38-0
Result: England win by seven wickets
Series: England lead the five-match series 1-0
Man of the match: James Vince
Toss: England
Umpires: Wayne Knights (NZL) and Shaun Haig (NZL)
TV Umpire: Ash Mehrotra (NZL)
Match Referee: Andy Pycroft (ZIM).