Kohli smashed nine fours in his unbeaten 110-run knock to help the visitors achieve the target of 239 with 21 balls to spare at the R. Premadasa stadium in Colombo.
The series win came after India swept the preceding three-Test rubber 3-0, capping their domination of the home side which has been beset by injury and selection woes.
This was India’s second 5-0 whitewash in an away ODI series with Kohli’s men having blanked Zimbabwe in 2013.
Sri Lanka squandered the opportunity to salvage some pride, folding up for a below-par 238 in 49.4 overs after paceman Bhuvneshwar Kumar grabbed a career-best 5-42.
“It’s quite amazing to have won the series 5-0. We always thought the shorter format is going to be much more challenging,” said Kohli.
“The youngsters and the spunk on the field has worked for us. All round, it’s been a complete series for us. We’ve been playing some good cricket.”
The Indians had a shaky start but Kohli anchored the innings with a 99-run partnership with Manish Pandey (36) for the third wicket.
He also put on 109 runs with Kedar Jadhav who scored a fine 63 off 73 balls.
Kohli, 28, looked in sublime form, hitting Milinda Siriwardana for three fours in an over to bring up his half-century.
– Kohli, Dhoni milestones –
The right-hander went on to complete his 30th ODI century, equalling former Australian captain Ricky Ponting’s tally.
Only Indian great Sachin Tendulkar has scored more centuries in the 50-over game with 49 tons.
Earlier, Kumar made the most of the conditions, reducing Sri Lanka to 40-2 before Lahiru Thirimanne (67) and Angelo Mathews stitched together a 122-run stand for the fourth wicket to steady the innings.
The dismissal of the two set batsmen triggered a collapse that saw the hosts lose seven wickets for 53 runs.
“It is a very difficult time for us. We were not up to the standard,” said Sri Lankan skipper Upul Tharanga.
“We lost a few early wickets. Thirimanne and Mathews had a good partnership. At one stage we were looking at 260-270. Unfortunately we collapsed again.
“We have to improve all three departments, especially our batting. We couldn’t get those big scores in all five games. We lost a few main players, but still as a captain I feel we didn’t play to our standard.”
Mathews gave an easy catch to wicketkeeper Mahendra Singh Dhoni off spinner Kuldeep Yadav (1-40) after making 55 off 98 deliveries.
Thirimanne, who hit three fours and a six in his 102-ball knock, was bowled by Kumar, the man of the match.
Dhoni passed a career milestone when he stumped Akila Dananjaya (four) off the bowling of leg-spinner Yuzvendra Chahal, his 100th in ODIs.
Dhoni became the first to achieve the feat, surpassing former Sri Lankan wicketkeeper Kumar Sangakkara who had 99 stumpings to his credit.