Sri Lanka to 99 for five in reply to the West Indies first innings total of 204 at the stumps on the second day of the day/night third Test.
Dowrich led Windies with an unbeaten half-century as the host from 53 for five to reach stumps at 132 for 5 on a rain-hit opening day.
West Indies hold on to secure a draw on the fifth day of the second Test against Sri Lanka.
Sri Lanka recovered from a top-order collapse to set up an intriguing final day in St Lucia.
Hosts bowled out for 300 after visitors agree to play under protest following ball-tampering row.
Only 42.3 overs were possible due to intermittent showers, just enough time for the opener to score a fifty.
Ton-up Chandimal helps Sri Lanka score respectable 253 against West Indies.
Sri Lanka are going to be without Angelo Mathews and Lahiru Gamage, who have both gone home for different reasons.
Mendis fought hard with a 210-ball 102 but spinners helped the hosts wrap up the victory just after Lunch on day 5.
The opener was unbeaten on 94 at stumps but West Indies chip away, with Sri Lanka three down to chase down a world record score of 453.