New Zealand needed 53 runs off 45 balls to reach a revised target of 263.
Anderson and Ronchi rode their luck in a 43-run, 33-ball stand which brought New Zealand within touching distance of victory.
Anderson had a blatant edge behind ignored by umpire Brent Bowden off Rahat Ali. Pakistan had used their review on an unsuccessful Kane Williamson lbw. Anderson seized on the Pakistan fury with consecutive sixes on his way to 35 off 29 balls.
Ronchi made 20 off 21 balls, an innings that included a top edged skyer which found turf between a Bermuda Triangle of fielders converging at third man.
Auckland's four-seasons-in-one-day weather punctuated a plot in which both teams fortunes ebbed and flowed like the rain sweeping the ground intermittently.
New Zealand played their ace through a record second-wicket partnership of 159 against all countries in ODIs from Martin Guptill (82 off 81 balls) and Williamson (84 off 86 balls).
At 165 for one in the 27th over New Zealand had the advantage originally chasing 291 to win; 15 runs and 13 balls later Pakistan resurged with both batsmen out, courtesy of the part-time leg spin from captain Azhar Ali.
Similarly, Pakistan's trump card was a 134-run third-wicket stand between Mohammad Hafeez and Babar Azam before they were bowled out for 290 in 47.3 overs. They lost their last seven wickets for 75 runs. The total was the fifth highest first innings in 70 ODIs at the ground, but an insurmountable haul had become a realistic chase.
By the time the rain was heavy enough for the players to exit, New Zealand were 210 for five in the 36th over. That placed them eight runs ahead of Pakistan under the Duckworth-Lewis Method, but the attack and counterattack continued.
The visitors continued on from the victorious batting platform they set in the recent T20.
They reaped the benefits of controlling their strokes, particularly towards the 57m backyard-length straight boundaries.
Led by Hafeez and Azam, they picked off deliveries with discretion rather than trying to smear every ball like a samurai swordsman distracted by a wasp. That caused New Zealand to make four bowling changes at the Walters Rd end from overs nine to 15, rolling through Trent Boult, Corey Anderson, Mitchell Santner and Grant Elliott.
Azam made his highest ODI score of 83 off 77 balls before cutting Henry to Guptill at point, his third catch of the innings after being declared fit to play on his twisted ankle.
He ended with four catches, equalling the New Zealand ODI record by a fielder, held by seven other players.
Hafeez eased to 76 off 60 balls by the end of the 23rd over before heaving Santner to Adam Milne at long leg.
That was the highlight of Santner's bowling allotment. He conceded 56 runs from five overs, his most expensive figures in 11 ODI bowling innings. Balletic footwork from the Pakistanis gave them the room to plunder four sixes and three fours allowing breathing room for just eight dot balls.
To New Zealand's credit, they hauled Pakistan back from 227 for four in the 34th over (a run rate of 6.78) with a spell of 65 balls which saw three wickets fall for 55 runs.
Matt Henry was the best of the New Zealand attack, further cementing his consistent ODI reputation with two for 44 from 10 overs. He was the only bowler to concede less than five runs per over.
Elliott also provided his Forrest Gump-like box of deliveries on his way to none for 55. Batsmen were never sure of what they were going to get, least of all non-striker Mohammad Rizwan who was run out for 16 when Elliott deflected a Sarfaraz Ahmed drive onto the stumps.
Sarfaraz gave the innings brief momentum as part of 41 off 49 balls but they lost impetus protecting the lower order in the latter overs.
Three Milne wickets for 49 mopped the tail.
- By Andrew Alderson at Eden Park
