Their 236-run stand is New Zealand's highest partnership in an ODI chase, the second-best first-wicket stand overall and only the third 200-plus effort by New Zealand openers in ODIs.
Guptill reached 116 off 138 balls for his eighth ODI ton while for lefthander Latham his 111 off 116 deliveries was his first, the pair's performance helping New Zealand level the series and take it to a decider on Friday night at the same venue.
Having restricted Zimbabwe, who had chosen to bat first, to 235 for nine, on a pitch which held few terrors for batsmen, New Zealand put themselves in charge of the contest.
''We came in wanting to win, we weren't good enough in last game and we really stepped it up today," Guptill said.
''Tommy and I had a great partnership to finish it off."
Guptill felt it was a pitch where if batsmen got themselves in they could prosper.
For Latham there was satisfaction at ''finally getting the monkey off the back", having made only one half century previously in his ODI career.
''Gup was a big influence in that, he kept me level-headed. I just tried to knock it off 10 runs at a time," Latham said.
The pair of tons take to 14 the numbers scored by New Zealand this year, easily the country's best and it was New Zealand's seventh 10-wicket win.
The only other occasion New Zealand openers both made centuries was James Marshall and Brendon McCullum against Ireland in 2008 when they put on 274.
The one other 200-plus opening stand was in Bulawayo against Zimbabwe, in 2005, by Stephen Fleming and Lou Vincent.
Guptill's century took him level with Fleming and trailing only Nathan Astle (16) and teammate Ross Taylor (15).
A spirited 100 not out from Sikander Raza, who shared a Zimbabwe ninth wicket record of 89 with seamer Tineshe Panyangara, put some substance into an otherwise ordinary batting display by the hosts.
Raza's third one-day hundred was loaded with spirit as he dug Zimbabwe out of a hole at 68 for five. His runs came off 95 deliveries, from which he struck four booming sixes.
It was a contestable point whether captain Elton Chigumbura made the right decision.
After all, Zimbabwe had won the first ODI electing to send New Zealand in and chase down 303 so it must have been tempting to stick with the routine that had worked two days earlier.
The only other batsmen to make a contribution were lively opener Chamu Chibhabha with a brisk 42, and Sean Williams, who added 60 with Raza for the sixth wicket.
New Zealand's bowling, problematic in the first ODI, was better, with hostility from Mitchell McClenaghan, tidy work from medium pacer Grant Elliott and offspinner Nathan McCullum and a good return for legspinner Ish Sodhi, who finished with three for 38 off his 10 overs.
Some of the New Zealand fielding was less than impressive.
Sodhi and Colin Munro - replacing Jimmy Neesham in the only change from the opening ODI -- slipped up badly off the luckless McClenaghan, which cost two boundaries, and substitute fielder Ben Wheeler spilling a regulation catch at cover off captain Kane Williamson, when Raza was on 67.
