England snared three quick wickets with spin but New Zealand's batters frustrated the tourists with their resistance on day three of the second Test in Wellington after Ben Stokes enforced the follow-on.

New Zealand were 3-202 in their second innings at stumps on Sunday, needing only 24 runs to make England bat again at the Basin Reserve.

Kane Williamson (25 not out) and Henry Nicholls (18 not out) held firm after Jack Leach triggered a batting collapse that netted 3-18.

New Zealand resumed after tea on 0-128, with openers Tom Latham and Devon Conway pushing their partnership to 149 runs before Leach made the breakthrough.

The spinner found a thick inside edge which careened off Conway's pad and looped over to short leg, where Ollie Pope dived forward to take the catch and remove the batter for 61.

The wicket shifted the momentum back to England, with Latham soon out lbw for 83 trying to sweep Joe Root.

Number four Will Young was bowled for eight by Leach, having managed two in the first innings, leaving New Zealand 3-167.

Williamson and Nicholls rode their luck through the final hour but strode off unbeaten, with New Zealand having some hope of setting England a challenging fourth innings chase.

New Zealand were bowled out in the morning session for 209 in reply to England's first innings of 8-435 (dec), the Black Caps falling 27 runs short of avoiding the follow-on.

Visiting skipper Stokes had little hesitation sending the hosts back in to bat on an overcast morning but Latham and Conway survived 19 watchful overs to lunch and then the entire middle session to tea.

New Zealand started the day on 7-138 in their first innings, still needing 98 runs to avoid the follow-on.

They briefly held hope of mowing the runs down as tail-ender captain Tim Southee went on a six-hitting spree in an entertaining knock of 73 off 49 balls.

Southee smashed Leach for three sixes in an over, the second bringing up his fifty from 39 deliveries and sending the ball onto scaffolding behind the long-on fence.

Leach dropped Southee when he slogged Stuart Broad to just in front of the fine leg rope when on 71.

But the spinner's anguish lasted only one ball as Southee was caught by Zak Crawley at midwicket after another top edge.

That ended an excellent 98-run partnership with wicketkeeper Tom Blundell and the match quickly turned.

Broad finished with 4-61, with Anderson (3-37) and Leach (3-80) also contributing.

England assistant coach Paul Collingwood defended Stokes's decision to enforce the follow-on.

"We're in a good position still," he said.

"The skipper wasn't thinking of not enforcing, just taking the positive approach and trying to win it today.

"Hard toil, but this wicket has done plenty in the morning session."