England skipper Ben Stokes already enjoyed a dominant position at the start of play but held off the declaration until Root secured his 36th hundred and was dismissed for 106 with the team on 427-6.
New Zealand made a stuttering start to their chase for the 583 runs that would secure them an unprecedented victory when Chris Woakes bowled Devon Conway through the gate for a duck.
Woakes deepened their woes when he had Kane Williamson caught behind off a thin edge for four before Brydon Carse chipped in with a brilliant caught-and-bowled dismissal of New Zealand captain Tom Latham for 24.
Carse continued his rich vein of form by sending back Rachin Ravindra, caught behind for six, just as the rain started to fall to bring up lunch five minutes early.
Daryl Mitchell will resume on 20 not out alongside Tom Blundell, who had yet to score, and New Zealand still 524 runs from their improbable target.
England had resumed on a blustery morning at Basin Reserve on 378-5 looking to quickly inflate their already imposing lead of 533 before sending the Blacks Caps in to bat.
The orthodox Root has not been the most natural player of the "Bazball" style of aggressive batting England have played under coach Brendon McCullum.
The 33-year-old, though, showed a flash of creativity to secure his 127-ball century with a glorious reverse-ramp for the 10th of the 11 fours in his knock.
Root edged behind to end the innings soon afterwards, Stokes racing off the field unbeaten on 49 keen to get his seamers out to get stuck in to the Black Caps with an unassailable 2-0 series lead in sight.
