The first four days' play had been severely affected by rain, wet ground conditions and bad light, but surprisingly the final day stayed clear despite a 30-minute delayed start.
Overnight centurion Tom Latham and Watling continued accumulating runs easily and took their side past Sri Lanka's first-innings total of 244.
Paceman Tim Southee struck twice to get into the Sri Lankan tail as New Zealand edged close to a series-levelling victory on day five of the second rain-hit Test on Monday.
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Latham, batting on an overnight 111, was brisk at the start but mostly risk-free. The tourists were 196 for four at stumps, still trailing Sri Lanka by 48 runs. "It's just that having different options to different bowlers". Their bowlers provided them with the early strikes they needed, reducing Sri Lanka to 32 for five before lunch. Watling, too, grew on confidence an opened his arms against the lose deliveries as he went on to share an unbeaten stand of 70 with Latham. A de Grandhomme outswinger saw the end of Mathews, lured into offering his bat and watching the edge go to slip, while Mendis got a peach of a delivery from Will Somerville, drifting, spinning and shooting between bat and pad to smash into the stumps.
A vicious bouncer to the left handed Embuldeniya saw a chance balloon to Williamson in the gully, the last man out for five, Sri Lanka all out for 122. Even a review couldn't save him, with three reds meaning the on-field decision was upheld and he had to be on his way, ending a stand of 143.
Grandhomme continued to play with his attacking mindset and hammered two sixes and a boundary in Lasith Embuldeniya's over to complete his half-century off just 45 deliveries.
De Grandhomme started briskly enough, but picked up the pace significantly after the tea break.
Watling (81*) and Grandhomme (83*) will resume New Zealand's inning from 382/5 on day five.