New Zealand, who went into the match ahead 1-0 in the two-Test series, were 183 for five with Kane Williamson on 48 and BJ Watling 14.
There would be no Brendon McCullum heroics to save the day as he did against India with a triple century on the same ground a year ago.
This time McCullum was gone for 22 to go with his first innings duck as New Zealand's top order folded rapidly after Tom Latham and Hamish Rutherford had produced a solid opening stand of 75.
The New Zealand opener could not resist slashing when peppered with short-pitched deliveries and was caught by Dinesh Chandimal waiting at third man.
Latham, who had looked assured on a pitch that has flattened out to offer the bowlers little assistance, became unsettled by the loss of his partner.
After a brief period of shuffling he followed Rutherford from the field caught behind for 35. Ross Taylor quickly joined them when he was bowled by Rangana Herath without scoring.
New Zealand referred the dismissal to the third umpire in vain as replays upheld the decision.
Jimmy Neesham (19) also went leg before wicket, although in his case he was initially given not out but the decision overturned after a Sri Lanka referral.
New Zealand were then just 24 runs ahead with five wickets in hand leaving Williamson, who had a reprieve on 29 when Herath spilled a caught and bowled opportunity, and Watling to take them through to tea.
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