Rayudu scripted an elegant knock of 124 and formed backbone of Hyderabad innings associating with Anirudh Singh (50) to put up 56 runs for the third wicket after the hosts were reduced to 48 for two.
In-form Arjun Yadav joined Rayudu and the duo had shown the needed aggression to accelerate the scoring rate with fluent drives and sharp cuts on either sides of the wicket adding 161 runs for the fifth wicket before Yadav went down to speedster Sumeet Mathur for a well made 52.
Rayudu took the battle further and displayed some good stroke play picking up 15 fours in a space of 178 balls to script a sparkling innings of 124 on a chilly Christmas day before Sumeet Mathur dismissed him.
After Rayudu's dismissal at 288, the hosts continued its dominance of the game and coasted to 323 at close with Fiaz Ahmed on 36 and Vishnuvardhan on 1 at crease.
For Rajasthan, speedster Sumeet Mathur claimed 3 for 91 while Sanjeev Sharma and Md Aslam took two wickets apiece.
Hyd gains two points from drawn match