The tourists ended the day at 8-208, still 68 runs short of their 275-run target and with the pitch offering significant assistance to the spinners, as Sri Lanka homed in on the win with just two wickets needed on Monday.
Ravindra has been fighting a lone battle for New Zealand. The left-hander remained unbeaten on 91 at stumps on Sunday and could become the first New Zealander to score a hundred in Galle.
Ravindra batted with a clear game plan, combining solid defence with an effective use of both the conventional and reverse sweeps to find scoring opportunities.
He also capitalised on a rare loose delivery from part-time spinner Dhananjaya de Silva, dispatching the full toss for six.
Chasing 275 was never going to be easy for New Zealand, and Prabath Jayasuriya made life difficult for the batsmen.
He claimed the crucial wicket of Kane Williamson, enticing the experienced player out of his crease before getting the ball to spin away slightly, allowing Kusal Mendis to complete a sharp stumping.
Ravindra found support in wicketkeeper Tom Blundell, and the pair added 56 runs for the fifth wicket.
But Jayasuriya struck again, producing a beauty to bowl Blundell around his legs. Soon after, he dismissed Glenn Phillips, who posed a threat with his aggressive hitting, caught at second slip.
Play on Saturday was halted due to Sri Lanka's presidential election, but on Sunday, Sri Lanka resumed their innings at 4-237.
Angelo Mathews went on to register another half-century, taking the home team's lead past 250.
The day's bowling honours belonged to New Zealand left-arm spinner Ajaz Patel, who finished with 6-90.
He was well-supported by fast bowler William O'Rourke, who took three wickets, adding to his five-wicket haul from the first innings to finish with eight in the match.
Sri Lanka will be eager to pick up the final two wickets quickly on the fifth morning, but New Zealand will hold onto hopes of a slim chance with Ravindra still at the crease.
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