The home team went to stumps on 223-2, still trailing by 215 runs, after Duckett struck a forceful 113 while Jacob Bethell was unbeaten on 74 when the players walked off at stumps on the second day.
Ben Stokes had earlier finished with figures of 4-70 in 21 overs as the Black Caps were all out in the second session as the tourists lost 10 wickets for 121 runs after a 317-run opening stand between Tom Latham and Devon Conway on the opening day.
Stokes also went past to the 250-wicket milestone as the home captain cemented his place as one of the game's premium allrounders in a Test that he returned after being suspended due to breaking a team curfew.
The skipper was well supported in the field on another scorchingly hot day in Nottingham with Jofra Archer taking 2-75 while spinner Shoaib Bashir finished with figures of 2-105.
New Zealand confirmed midway through the evening session that seamer Blair Tickner has been ruled out for the remainder of the Test due to concussion and will be replaced by Zak Foulkes.
Tickner, batting at No. 10, was hit on the helmet by the third ball he faced, prompting a delay while he was checked for concussion symptoms but eventually continued to bat.
He then bowled three wicketless overs for 21 runs but did not return to the field after the tea interval due to nausea.
New Zealand took firm control of the series-deciding third Test against England after a superb opening day at Trent Bridge, finishing on 361/4 after choosing to bat first.
Ben Stokes will return as England captain in of four changes to the home team's starting line-up for the third and deciding Test against New Zealand that starts at Trent Bridge on Thursday.
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.
