The current series is tied at 1-1, with Sri Lanka winning the opening Test by an innings and 239 runs in Colombo and India coming back strongly to clinch a 170-run victory in the second match in Galle.
The Sri Lankan captain said his bowlers would look for early breakthroughs to keep pressure on the India's middle-order batsmen, who have yet to fire in the series.
Virender Sehwag and Gautam Gambhir played key roles in India's win, adding 167 for the opening wicket in the first innings and 90 in the second. Sehwag was named man of the match for scoring an unbeaten 201 and 50.
"Sehwag batted really well and took his chances in Galle. India are getting some good starts and that is something we will think about," said Jayawardene.
"If we get early breakthroughs we can manage to keep the rest of their batsmen pretty quiet.
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If we keep that pressure