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.
England face an uphill battle in the second Test against New Zealand at The Oval after a difficult second day left them well behind in the contest despite a promising start to the match.
England seamer Sonny Baker was relieved with his debut in the second Test against New Zealand at The Oval, after a promising display on day one.
New Zealand's middle order and England's inexperienced attack traded blows on an engrossing opening day of the second Test at The Oval, with the tourists closing on 291 for 7 after recovering impressively from a precarious position of 107 for 4.
New Zealand captain Tom Latham has confirmed that Henry Nicholls will step into the vacant number 3 role for the second Test against England starting at the Oval on Wednesday.
