A resolute half-century from Ben Foakes pushed England 368 runs ahead of New Zealand with two wickets in hand on an absorbing third day of the opening Test in Mount Maunganui on Saturday.

Foakes was dismissed for 51 late in the second session as the tourists reached 349-8, leaving them favoured to win the fast-moving day-night encounter.

The Black Caps will have ample time to chase down a target but their batters will likely need to first negotiate the threat of a swinging new pink ball under lights in the final session on Friday.

No team has successfully chased more than 345 in the fourth innings of a Test in New Zealand.

Wicketkeeper Foakes provided composure after his top order swung freely in the opening session, their big-hitting powering England to 237-6 at tea, having resumed at 79-2 overnight.

Ollie Pope scored 49, Joe Root 57 and Harry Brook 54, all playing the sort of aggressive knocks that have become a hallmark of England on the way to winning nine of their last 10 Tests.

Captain Ben Stokes contributed a lusty 31, in the process overtaking his coach Brendon McCullum as the outright record holder for the most sixes struck in Test cricket.

Stokes hoisted the 108th six of his career when he hooked seamer Scott Kuggeleijn over fine leg.

He hit one more before being stumped off spinner Michael Bracewell, typically trying to force the pace.

Most other England wickets fell when taking risks, most notably Root, who for the second time in the Test was caught in the slips after mis-timing a reverse sweep.

New Zealand's Neil Wagner was targeted ruthlessly, going to tea with figures of 2-104 -- the most runs any bowler has conceded from their first 11 overs of an innings in Test history.

Wagner paid a heavy price for persisting with short-pitched bowling, conceding 12 fours and six sixes, the vast majority through cross-batted shots.

The left-armer's last over cost 18 runs as Brook opened his stance and used a baseball technique to swat the 36-year-old for four boundaries.

Wagner claimed the first two wickets of the day, luring false shots from nightwatchman Stuart Broad (7) and Pope.

Brook and Root put on 81 for the fifth wicket in less than 11 overs before Brook was caught behind off Blair Tickner (3-55), who has taken four wickets in his debut Test.