New Zealand edge Australia in T20 run-fest
Both sides took advantage of University Oval's short boundaries in a thrilling match that featured 30 sixes and 434 runs at an average of 10.9 an over.
Marcus Stoinis starred for the Australians with 78 from 37 balls but Guptill's 97 from 50 laid the foundation for New Zealand's win.
Black Caps spinner Mitchell Santner also shone amid the batting fireworks, taking four for 31, while Australian paceman Kane Richardson managed three for 43.
Neesham also scored an undefeated 45, including six sixes.
The result puts New Zealand 2-0 up in the five-match series, on the brink of a shock win over the world's second-ranked Twenty20 team.
Guptill's innings gave him the record for the most sixes in Twenty20 internationals with 132, taking him past India's Rohit Sharma on 127.
The 34-year-old clubbed the ball over the boundary eight times, bludgeoning all comers in the Australian attack.
He fell just short of his third Twenty20 century after being caught trying to hit a Daniel Sams delivery out of the ground.
- Steady Williamson -
Guptill averaged only 17 in the recent series against the West Indies and Pakistan, then managed just 11.5 in the domestic competition before picking up a hamstring injury.
Pressure on the opener intensified when he made a duck in the first match against Australia on Monday, with calls for uncapped Finn Allen to join the squad.
But he answered his critics with a return to his big-hitting best, bringing up 50 off 27 balls, with eight boundaries, including four sixes.
Guptill insisted he had not changed his approach during the game-turning innings. "I just went out and tried to do the best I could -- fortunately for me it came off," he said.
While Guptill provided fireworks at one end, Kane Williamson was steady at the other, scoring 53 off 35 balls.
Australia made a solid start in reply, despite skipper Aaron Finch continuing to struggle for runs when he was dismissed for 12.
The tourists were 87 for two at the halfway mark, with rookie batsman Josh Philippe scoring 45 from 32 balls.
He departed as part of a mid-innings collapse that saw Mitch Marsh and Ashton Agar out for first-ball ducks as Santner claimed three wickets in an over.
But the heroics from Stoinis and Sams -- who scored 41 from 15 balls -- were not enough to get Australia over the line.
M. Guptill c Stoinis b Sams 97
T. Seifert c Finch b K.Richardson 3
K. Williamson b Zampa 53
J. Neesham not out 45
G. Phillips b J.Richardson 8
D. Conway c Zampa b k. Richardson 2
M. Santner c Maxwell b Richardson 0
T. Southee run out (Wade/Sams) 6
K. Jamieson not out 0
Extras (lb1, w4) 5
Total (7 wickets; 20 overs) 219
Did not bat: Ish Sodhi, Trent Boult.
Fall of wickets: 1-20 (Seifert), 2-151 (Guptill), 3-173 (Williamson), 4-190 (Phillips), 5-198 (Conway), 6-199 (Santner), 7-213 (Southee)
Bowling: Sams 4-0-46-1 (w1), Agar 3-0-30-0, J. Richardson 4-0-39-1 (w1), K. Richardson 4-0-43-3 (w1), Zampa 4-0-43-1 (w1), Stoinis 1-0-17-0
M. Wade c Williamson b Southee 24
A. Finch c Phillips b Sodhi 12
J. Philippe c Conway b Santner 45
G. Maxwell c Sodhi b Santner 3
M. Stoinis c Southee b Neesham 78
A. Agar c Conway b Santner 0
M. Marsh c Seifert b Santner 0
D. Sams c Phillips b Neesham 41
J. Richardson not out 4
K. Richardson not out 0
Extras (w7, nb1) 8
Total (8 wickets; 20 overs) 215
Fall of wickets: 1-34 (Wade), 2-70 (Finch), 3-87 (Maxwell), 4-112 (Philippe), 5-113 (Agar), 6-113 (Agar), 7-205 (Sams), 8-211 (Stoinis)
Bowling: Southee 4-0-47-1 (1w), Boult 4-0-30-0 (2w), Jamieson 4-0-56-0 (1w, 1nb), Santner 4-0-31-4 (1w), Sodhi 3-0-41-1, Neesham 1-0-10-2
Result: New Zealand win by four runs
Series: New Zealand lead the five-match series 2-0
Man of the match: Martin Guptill (NZL)
Umpires: Shaun Haig (NZL), Chris Gaffaney (NZL).
TV umpire: Chris Brown (NZL)
Match referee: Jeff Crowe (NZL)