England is chasing a winning target of 296 to sweep the series after dismissing New Zealand for 326 at tea on Sunday with Jack Leach taking 10 wickets in the third test at Headingley.
The England spinner claimed 5-66, including the final wicket of Trent Boult (4), to go with his 5-100 in the first innings.
Tom Blundell ran out of partners and was 88 not out at the end of New Zealand's second innings. He shared another impressive partnership with Daryl Mitchell (56), who was trapped leg before wicket in the afternoon by pacer Matthew Potts (3-66). The pair put on 113 for the sixth wicket.
