New Zealand took four wickets but Karunaratne and Thirimanne made vital contributions to pilot the hosts to a six-wicket win.
India finished first day on 297 for 5 after Windies dent early blow.
Steven Smith takes centre stage again on day of high drama as Australia give themselves a chance.
Having got the 268-run target from New Zealand, Sri Lanka have started strongly as Sri Lanka have reached 133/0 at stumps on Day 4.
Jofra Archer, Stuart Broad impresses for England as Australia suffer top-order collapse on rain-marred third day of 2nd Test.
He beat Mike Hesson and Tom Moody to the appointment, and will stay in charge until the T20 World Cup in 2021.
A fighting half-century by wicketkeeper-batsman B.J. Watling helped New Zealand to take a highly competitive lead of 177 at stumps.
Australia ended day 2 at 30/1 after England bowled out for 258.
Ajaz Patel picked up a five-for while Lakmal and Dickwella shared a crucial unbeaten stand of 66 to keep the home side afloat.
Jofra Archer receives England Test cap before rain washes out Day 1 of second Ashes Test