After the start of the day-night match was delayed by an hour and 20 minutes due to persistent rain, further bad weather during the West Indies innings reduced the game to 26 overs-a-side.
Fast bowler Suranga Lakmal claimed three quick wickets as the tourists slipped to 24-3 before the rain break, and then became 42-4 soon after resumption.
Russell smashed three sixes and as many fours in 41 off 24 balls and left-handed Bravo chipped in with 38 during an entertaining fifth-wicket stand to retrieve the situation.
Sri Lanka swept the preceding Test series 2-0. The three one-dayers will be followed by two Twenty20 games.