The 21-year-old Wellalage, a left-arm spinner, came to bat at number seven to hit an unbeaten 67 after Sri Lanka slipped to 101-5 at Colombo's R. Premadasa Stadium.
He put on key partnerships including a 46-run eighth-wicket stand with Akila Dananjaya, who made 17, to take the attack to the opposition bowlers, who largely dominated the contest.
India's ODI team is boosted by the return of captain Rohit Sharma and Virat Kohli as the top guns took field.
Both Rohit and Kohli retired from T20 internationals after India's World Cup triumph in Barbados in June, and the team won that format series 3-0 in Sri Lanka on Tuesday under Suryakumar Yadav, who is not in the 50-over side.
Batting collapses made Sri Lanka suffer in the T20 matches and another scare was on the cards when the home team lost half their side in the 27th over after in-form Pathum Nissanka departed for 56.
Mohammed Siraj struck first with the wicket of Avishka Fernando for one and the top and middle-order soon faltered including skipper Charith Asalanka out for 14.
But Wellalage batted with grit as he picked the gaps and was excellent in running between the wickets to put India's fielders under pressure.
Janith Liyanage and Wanindu Hasaranga made useful contributions with 20 and 24 runs.
Left-arm quick Arshdeep Singh and left-arm spinner Axar Patel took two wickets each.
Sri Lanka have handed an international debut to pace bowler Mohamed Shiraz after quicks Matheesha Pathirana (shoulder) and Dilshan Madushanka (hamstring) were ruled out of the series with injuries.
For India, KL Rahul returns as wicketkeeper-batsman and Shreyas Iyer also makes a comeback.
