Overton stars with bat and ball as England eye New Zealand whitewash
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New Zealand were 168-5 in their second innings, a lead of 137, with paceman Matthew Potts having taken 2-20, when rain cut short Saturday's third day of the third Test.
But with England having chased down 299 inside a day to win the second Test and go 2-0 up in the three-match series, the Black Caps still had plenty to do if they were to avoid a whitewash, with two days' play remaining in Leeds.
Earlier, Jonny Bairstow, fresh from his match and series-winning century at Trent Bridge, extended his overnight 130 not out to 162.
He had been joined by Overton on Friday, with the hosts in dire straits at 55-6.
But their England record seventh-wicket stand of 241 was the cornerstone of an eventual total of 360 -- a first innings lead of 31.
Black Caps opener Will Young then fell cheaply before a second-wicket stand of 97 steadied the tourists.
New Zealand captain Kane Williamson cover-drove the opening ball of opposing skipper Ben Stokes's first bowling stint this Test for four.
Tom Latham forced the all-rounder away for his sixth boundary before a single took him to a 70-ball fifty in a series where his previous best score had been a meagre 26.
Latham, dropped by Joe Root in the slips on 72, fell to the first ball after tea.
The towering Overton, in for injured England great James Anderson, had him caught behind for 76 by stand-in wicketkeeper Bairstow, with first-choice gloveman Ben Foakes sidelined by a stiff back on Saturday.
Devon Conway turned Root's first ball after the break off his pads, only for Ollie Pope to hold a superb one-handed catch at short leg.
Conway's exit sparked a mini collapse that saw three wickets lost for just nine runs, with New Zealand's 152-2 quickly transformed into 161-5.
Williamson casually flicked at Potts outside off stump to give Bairstow a simple catch, the star batsman throwing his head back in anguish following the end of a well-made 48 featuring eight boundaries.
Left-arm spinner Jack Leach, fresh from his 5-100 in the first innings, then deceived Henry Nicholls into offering a low return catch.
Daryl Mitchell, who has already hit three hundreds this series, was four not out when rain ended the day's play, with Tom Blundell unbeaten on five.
Overton had resumed on 89 not out at the start of play on Saturday.
But the 28-year-old never regained the fluency he had on Friday and it was no shock when Trent Boult, who had removed all of England's top three with a superb display of new-ball bowling, had Overton caught in the slips.
England's new leadership duo of Stokes and coach Brendon McCullum had urged the team to play with freedom after taking charge of a side that had won just one out of 17 Tests prior to this series.
Stuart Broad embraced the new approach by hitting Boult for 14 runs in three balls courtesy of two fours during a quickfire 42.
And one ball after Broad's exit, he holed out off spinner Michael Bracewell to end a brilliant 157-ball innings including 23 fours.
New Zealand 1st Innings 329 (D Mitchell 109, T Blundell 55; J Leach 5-100, S Broad 3-62)
England 1st Innings (overnight: 264-6)
A. Lees b Boult 4
Z. Crawley b Boult 6
O. Pope b Boult 5
J. Root c Blundell b Southee 5
J. Bairstow c Boult b Bracewell 162
B. Stokes c Williamson b Wagner 18
B. Foakes lbw b Wagner 0
J. Overton c Mitchell b Boult 97
S. Broad b Southee 42
M. Potts not out 1
J. Leach lbw b Southee 8
Extras (lb11, w1) 12
Total (all out, 67 overs, 348 mins) 360
Fall of wickets: 1-4 (Lees), 2-14 (Pope), 3-17 (Crawley), 4-21 (Root), 5-55 (Stokes), 6-55 (Foakes), 7-296 (Overton), 8-351 (Broad), 9-351 (Bairstow), 10-360 (Leach)
Bowling: Boult 22-4-104-4 (1w); Southee 23-2-100-3; Wagner 12-1-75-2; Bracewell 7-0-54-1; Mitchell 3-0-16-0
New Zealand 2nd Innings
T. Latham c Bairstow b Overton 76
W. Young c Pope b Potts 8
K. Williamson c Bairstow b Potts 48
D. Conway c Pope b Root 11
H. Nicholls c and b Leach 7
D. Mitchell not out 4
T. Blundell not out 5
Extras (b5, lb1, nb2, w1) 9
Total (5 wkts, 51.5 overs, 240 mins) 168
To bat: M Bracewell, T Southee, N Wagner, T Boult
Fall of wickets: 1-28 (Young), 2-125 (Latham), 3-152 (Conway), 4-153 (Williamson), 5-161 (Nicholls)
Bowling: Broad 14-2-45-0; Leach 13-5-26-1; Potts 9.5-2-20-2; Overton 9-2-34-1 (1nb, 1w); Stokes 4-0-30-0 (1nb); Root 2-0-7-1
Match position: New Zealand lead by 137 runs with five wickets standing