Jayawardene's 118 accounted for just under half of Sri Lanka's 242 all out in the third meeting of a five-match series, and India knocked off the runs to record a six-wicket win with 35 balls to spare.
While the 37-year-old became the fifth player to go past 12,000 ODI runs in Hyderabad with his 17th century, his team-mates struggled to offer support.
Only three other batsmen were able to get into double figures, something Jayawardene was critical of after the match.
"We need to be consistent in our overall game," he said in his post-match interview. "The way the Indians are playing, we need 300 to put them under pressure, and we are not there yet.
"They are putting us under lot of pressure, picking early wickets, putting us on the back foot straight away, and we are doing repair work after that."
India captain Virat Kohli was understandably delighted with a fifth ODI triumph in a row, and praised his side's all-round performance to finish the series off with two matches to play.
"That was a brilliant performance," he said. "Especially with the ball, given we were one bowler short, to restrict them to 242 was fantastic."
The two sides now travel to Kolkata for the fourth match of the series, with the final game in Ranchi on November 16.