hit a chanceless maiden ODI ton, as India ran down Sri Lanka's 275 for 8 with six wickets in hand and 33 balls to spare. Rayudu and Shikhar Dhawan
put on 122 runs for the second wicket to set up the chase, and having come to bat in the seventh over, Rayudu was at the crease to hit the winning runs and finish on 121 off 118 balls.
Sri Lanka's bowlers were short on menace, but it had been the batsmen who erred first in the game. Early wickets in their innings made for a measured recovery, and though Angelo Mathews
' unbeaten 92 pushed the score towards credibility, he lacked support from the middle order, as the team finished at least 30 runs light on a flat Motera surface, and with dew set to form later in the evening.
Rayudu arrived just as the Sri Lanka seamers appeared to be hitting a rhythm, but like they had done in the previous ODI, the India batsmen sought to lay low until the seam grew soft and the changes were rung in. Dhawan was handed had a life in the eighth over, when he was on 10. Lahiru Gamage seamed a length ball away and collected his outside edge, but the sound and the clear deviation escaped the umpire's notice, to Sri Lanka's disbelief.
Once the new-ball bowlers had finished their opening spells, the batsmen eased out of their vigil and gradually tightened their grip on the chase. The first acceleration came just as the asking rate clicked over six per over. Rayudu strode down the track to launch Suraj Randiv over long on in the 17th over, establishing what would become one of the major themes of his hundred: the effective use of his feet against the spinners.
By the 20th over, the pair had raised the run rate to above four an over, and the boundaries began to flow more easily. Both batsmen trusted the pace and bounce of the pitch, stepping out to crash balls in the arc between cover and midwicket, and using the crease to hit square when the bowlers were rattled off their lengths. Thisara Perera was blasted for 17 in one over - the most expensive in a seven-over stretch between the 19th and 26th that yielded 69 runs for India. Mathews switched his bowlers almost manically, attempting to tamp blaze that had so quickly grown into a wildfire, but as both batsmen completed half-centuries and surged ahead, India's momentum only grew.
Dhawan was eventually dismissed for 79 off 80, top-edging a sweep to give Seekkuge Prasanna the first of his three wickets, but at 140 for 2 in the 27th over, India were well in control. The new batsman Virat Kohli began to find runs into the outfield almost as easily as Rayudu, and the Sri Lanka bowlers seemed like little more than fodder.
Rayudu surged as he neared his milestone, hitting a remarkable six off a Dhammika Prasad short ball before depositing Randiv over the straight boundary soon after. He clipped one through square leg to breach triple figures for the first time, off 101 balls. The scoring rate only increased after that. Kohli had 49 from 44, before driving one straight to Randiv at cover. Suresh Raina slammed 14 from 6, but the game was long won before he had come in.
Earlier, Kusal Perera's inclusion had failed to ease Sri Lanka's opening woes as Umesh Yadav trapped him in front for a duck, in the first over. Tillakaratne Dilshan and Kumar Sangakkara were visibly short of rhythm in the early overs, but managed to set Sri Lanka off to a start, before two quick wickets fell.
Mathews came to the crease at 64 for 3, and forged a 90-run stand with Sangakkara that was steady, but unremarkable in style. Mathews employed the sweep to good effect, even venturing a slog-swept six off Ashwin in the 20th over, but both batsmen were largely content for the recovery to tick along. When Sangakkara reached his fifty off 73 deliveries, he had struck only three fours.
The Powerplay, taken in the 32nd over, brought the next innings stutter. Sangakkara took aim at a thigh-high Yadav full toss and hit it down an outfielder's throat. Prasanna's innings glinted briefly as he attempted to electrify the innings, but was soon undone playing his favoured sweep.
Sri Lanka continued to lose batsmen as they strove to attack, perhaps in the knowledge that Prasad at No. 10 was capable of helping Mathews see the innings out, but the setbacks muted the Sri Lanka captain. He seemed ready to unleash when he slammed Ravindra Jadeja for three consecutive legside fours, in an over that went for 20, but the back end of his innings was marked by restraint, even with a maiden ODI hundred on the cards.
Prasad's unbeaten 30 off 28 in a ninth-wicket stand saw Sri Lanka finish the innings with some semblance of respectability, but with the Indian batsmen in ace form, the visitors' score was thoroughly inadequate.
Andrew Fidel Fernando is ESPNcricinfo's Sri Lanka correspondent. @andrewffernando