Jamie Overton believes England are in the "box seat" after a pulsating third day of the third Test against New Zealand at Headingley.

Seeking a 3-0 whitewash with victory in Yorkshire, England claimed a lead of 31 runs as they were bowled out for 360.

Jonny Bairstow added to his overnight 130 to reach 162, five short of his best ever total for England in the longest format, while Overton missed out on a debut Test century when he was caught on 97.

New Zealand fell from 152-2 to 168-5 after a rain break in the evening session to leave Daryl Mitchell and Tom Blundell looking after a lead of 137 when rain stopped play.

Overton was understandably disappointed to narrowly miss out on a century, but believes his knock has helped give England the edge going into the final two days.

"It's been good fun. Obviously I was very disappointed getting out on 97, but I feel like I've contributed to the team," he told reporters.

"It's always a challenge when you first go into something, but I feel I've done okay. I'd like to take a few more wickets, but I'm more than happy to get 97. I didn't think I'd get anywhere near that, especially coming in at 55 for six.

"I think that last session put us right in the box seat. We would like to go back out there at the end but couldn't quite get out there with the covers needing time to get them off.

"But we're in a great position going into tomorrow and hopefully we can get the two early wickets, the two key wickets. But we feel like we're in a good place. And if we can get those two early, then we're in a great place to win the game."

The Headingley crowd was in particularly raucous mood on Saturday, and Overton credited England's swashbuckling approach as key to the electric atmosphere.

"I've definitely not experienced anything like that before," he added. "The closest I've had was a Surrey against Somerset game, Ryan Patel getting things going down at third man. That was loud but it was nothing like this.

"Ben Stokes has got the ethos of trying to be entertainers for everyone and he said in the changing room earlier that the way me and Jonny played had the crowd on the edge of their seats.

"That's entertaining cricket and that's what we want to be doing. I like to think I'm quite an entertaining cricketer."