England 360 (Bairstow 162, Overton 97) and 183 for 2 (Pope 81*, Root 55*) need another 113 runs to beat New Zealand 329 (Mitchell 109, Blundell 55, Leach 5-100) and 326 (Blundell 88, Latham 76, Mitchell 65, Leach 5-66)
Headingley: England need 113 runs with eight wickets in hand to complete another superb final-day victory against New Zealand in the third Test at Headingley.
Set 296 to win, England hurried along once again to reach 183-2 on day four.
Ollie Pope made 81 not out and Joe Root an unbeaten 55, putting on 132 after Alex Lees was run out for nine and Zak Crawley caught for a frantic 25.
After chasing 277 in the first Test and breathlessly pursuing 299 to win the second, victory in Leeds will give England a 3-0 series clean sweep over the World Test champions.
They would have hoped to earn themselves a smaller target when New Zealand resumed on 168-5 - 137 ahead - but were thwarted by Tom Blundell's 88 not out.
Blundell, who overturned an lbw decision on 52 and was dropped on 67, combined with Daryl Mitchell yet again for their fourth century stand of the series.
Mitchell fell lbw for 56 to the impressive Matthew Potts 50 minutes into the afternoon session before Jack Leach took the last four wickets to claim 5-66 and his first 10-wicket match haul in Tests.
Before this series, when England had won only one of their past 17 Tests, a chase of almost 300 would have looked way beyond them.
But they have been transformed under new coach Brendon McCullum and captain Ben Stokes to the point that anything now looks possible.
At Trent Bridge last week they had 72 overs to chase 299 and did so in 50.
With four sessions to reach their target on this occasion, they batted in slightly more measured fashion but still eased along at more than four an over, Joe Root reverse sweeping his first ball and later playing an outrageous scoop for six off pace bowler Neil Wagner.
New Zealand's only spinner, part-timer Michael Bracewell, was ineffective and seamers Trent Boult and Tim Southee were neutered by a lack of movement and a flat pitch.
Showers are forecast on Monday morning, but there should still be time for either side to force a win.