Playing just his third Test, India's number 3 was unbeaten on 131 at the close of play, while opener KL Rahul made 77 before he was forced to retire hurt as visitors batted out 73 overs.
Rahul and opening partner Yashasvi Jaiswal had given India a solid start with 47 before the latter was needlessly run-out for 32 after colliding with debutant spinner Keshara Nuwantha.
Padikkal then entered the fray in India's troublesome number 3 position, for his first Test in two years, and immediately looked comfortable as the left-hander raced to 21 from just 23 balls.
Rahul was quietly accumulating at the end and India went to lunch on a commanding 101-1 in 27 overs after Shubman Gill had won an important toss and opted to bat.
The visiting pair kept their wicket in tact for the entire second session and went to the tea interval on 197-1 with Padikkal on 84.
Rahul did not return for the final session as he suffered from cramp in the arm and skipper Gill was on hand to watch Padikkal to reach his maiden Test ton.
Sri Lanka left-arm spinner Prabath Jayasuriya removed India captain for 16 but Rishabh Pant (27 not out) kept Padikkal company as rain brought an early close to proceedings.
Sri Lanka allrounder Sonal Dinusha struck a maiden century but India took a firm grip on proceedings at stumps on a rain-shortened third day of the first Test in Galle.
India ended the second day of the first Test against Sri Lanka in complete control at 460/9 in their first innings.
India captain Shubman Gill feels the preparation time his team have had ahead of the first Test against Sri Lanka is important as they continue going through a transition.
Niroshan Dickwella is set to return from the wilderness to Sri Lanka's team for the first Test against India, starting in Galle on Saturday, with captain Dhananjaya de Silva backing the wicketkeeper to come good.
