The Black Caps closed on 252-3 in their second innings, with Nicholls unbeaten on 119 and Daryl Mitchell on 32 not out. The tourists are now firmly on course to level the three-match series after losing the opener at Lord's.
After taking a first-innings lead of 100, New Zealand suffered an early setback when England dismissed both openers. Tom Latham fell to Jofra Archer before Devon Conway edged Josh Tongue to slip, leaving the visitors on 28-2.
England's hopes of building pressure were dealt a major blow when wicketkeeper James Rew dropped Rachin Ravindra on seven. The missed chance proved costly as Ravindra and Nicholls combined for a crucial 161-run partnership that shifted the contest decisively in New Zealand's favour.
Nicholls, recalled following Kane Williamson's surprise retirement after the first Test, responded with a composed innings at No. 3. The left-hander mixed patience with positive strokeplay, while Ravindra recovered from his early reprieve to score a fluent 76.
The stand was eventually broken when Jacob Bethell trapped Ravindra lbw attempting a sweep. By then, however, New Zealand were already in complete control.
Nicholls continued to frustrate England's attack and reached his 11th Test century from 136 deliveries, bringing up the milestone with his 14th boundary. His innings has put the visitors in a dominant position heading into day four.
Earlier, England were bowled out for 291 despite a defiant unbeaten 50 from Matt Fisher, who shared a last-wicket stand of 53 with fellow debutant Sonny Baker.
Matt Henry was the chief architect of England's downfall, claiming 5-80 for his seventh Test five-wicket haul. Jordan Cox, Jofra Archer and Tongue were among his victims as New Zealand secured a valuable first-innings advantage.
With a huge lead already established and seven wickets remaining, New Zealand head into the fourth day firmly in control and within touching distance of drawing the series level.
Jos Buttler has been retained in England's squad for the five-match T20I series against India while James Coles has earned his maiden international call up in an enlarged 17-man group.
Matt Henry says his job is to be effective and not "look like a hero" after bowling New Zealand to victory in the second Test against England at the Oval to level the three-match series at 1-1.
Ben Stokes and Gus Atkinson have been cleared to return to England's squad for the third and deciding Test against New Zealand, after both players received written warnings following an investigation into a breach of team protocol.
New Zealand claimed a dominant 253-run win in the second Test against England to take the series to 1-1 ahead of the deciding game in Nottingham.
