Buttler hit 129, his hundred coming off 66 balls - the second fastest ever for England and five balls more than the 61 he took to blast a ton against Sri Lanka last year.
England's previous best ODI total was 391-4 against Bangladesh in Nottingham in 2005.
Buttler also shared in a world record seventh wicket ODI stand of 177 with Adil Rashid (69) as a new-look England put memories of their dismal World Cup group stage exit earlier this year firmly behind them.
The omens had not looked good for England as opener Jason Roy fell to the first ball of the day.
But Root, firstly with Alex Hales (20) and then Eoin Morgan (50) set about a recovery, taking the attack to New Zealand.
Root's hundred came off 71 balls before he fell for 104, one of four wickets for Trent Boult.
Buttler and Rashid then took over, their partnership surpassing the previous best seventh-wicket ODI stand of 130 by Zimbabwe's Andy Flower and Heath Streak against England in 2001.
New Zealand, who thrashed England the last time the teams met in an ODI in February, were set to start their reply, needing to surpass their previous best ODI total of 402 to have a chance of victory.
Original source: Buttler and Root lead fireworks against NZ