The hosts, who began the day at 99-1 in reply to Pakistan's 451, carried their first innings to 252-2 by tea before heavy rain wiped out the final session of play.
Just 46 of the stipulated 90 overs were bowled during the day, leaving a draw as the likely result with just 12 wickets having fallen over the first three days.
Sri Lanka will resume on Saturday trailing by 199 runs with eight wickets in hand.
Only the retired trio of India's Sachin Tendulkar, with 51 centuries, Jacques Kallis of South Africa who had 45, and Ricky Ponting of Australia on 41, have scored more hundreds.
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Jayawardene, set to quit Test cricket at the end of this two-Test series, showed he was good enough to prolong his 17-year career as he survived an anxious start to hit an unbeaten 55.
The tried and trusted duo of Sangakkara and Jayawardene, whose partnership of 624 against South Africa in Colombo in 2006 remains a world record, have so far put on 108 for the third wicket.