Hooda brought up his 10th first-class hundred as the home sided reached 310/5 at stumps.
Deepak Hooda being preferred over both Sanju Samson and Shreyas Iyer has been a surprise.
The 15-member squad led by Roht Sharma features two wicketkeepers in Rishabh Pant and Dinesh Karthik.
Hooda has now been part of 16 successive wins for India, which is the longest unbeaten streak for any player since debut.
Opener Sanju Samson chipped in with a 30-ball 38, while Suryakumar Yadav remained unbeaten on 36.
Ashwin and Buttler will play for Royals, while Hooda and Krunal were bought by Lucknow Super Giants.
The IPL distributed the updated player list of 600 names to the franchises with the addition of ten new names.
Rahul, who himself made 91 off 50 deliveries, breathed a sigh of relief after Sanju's 119 failed to get Rajasthan Royals past the finish line against Punjab Kings.
Hooda had walked out of the team on the eve of Syed Mushtaq Ali Trophy T20 tournament after a spat with captain Krunal Pandya.