The modest chase looked far from a cakewalk, however, as the visitors slumped to 25 for two in the sixth over before Warner's century helped them romp home with seven overs to spare.
Warner found an able ally in George Bailey and the duo added 132 runs as the world champions went on to exact a modicum of revenge after being whitewashed in the preceding three-match test series.
Bailey (44), the top-scorer in the five-match series, missed his third successive fifty but Warner could not be denied his seventh ODI century for a total of 199 for five.
Leading the side in absence of regular skipper Steve Smith, who has returned home to rest ahead of a busy schedule, Warner played a captain's knock of 106 which made all the difference in the low-scoring contest.
The 29-year-old southpaw paced his knock according to team requirement and studded it with nine fours before being dismissed with his team seven runs from victory.
Earlier, Sri Lanka squandered their best start of the series to settle for a below-par score after Dinesh Chandimal, leading the side in absence of injured regular skipper Angelo Mathews, won the toss and opted to bat in the dead rubber at Pallekele.
Openers Dhananjaya de Silva (34) and Danushka Gunathilaka (39) raised 73 runs before the hosts lost three quick wickets to slump to 78 for three in the 16th over.
Kusal Mendis (33) added 43 runs with Upul Tharanga (15) but another mini-collapse followed soon.
Sachith Pathirana chipped in with 32 runs down the order before being the last man out in the 41st over.
The teams will now square off in a two-match Twenty20 series beginning on Tuesday.
(Reporting by Amlan Chakraborty in New Delhi; editing by Rex Gowar)
