The 29-year-old Uthappa blasted as many as 21 boundaries and one six en route to his second century this Ranji season, while Rahul, who struck 14 fours during his 154-ball innings, missed out on a well-deserved hundred.
The duo dominated the Assam bowlers, sharing a 194-run opening stand in 55.1 overs at the Holkar Cricket Stadium.
Ravikumar Samarth (39) and Manish Pandey (18) were at the crease when the stumps were drawn.
Earlier, Assam skipper Dheeraj Jadhav's decision to insert the opposition first after winning the toss backfired as his seam bowlers failed to exploit the Indore track, which is known to assist the pacers.
New ball bowlers Arup Das (16-5-49-0) and Krishna Das (17-3-44-0) bowled well initially but after first hour of play the pitch eased out and Uthappa and Rahul started playing more freely.
Assam's offspinner Swarupam Purkayastha also found the going tough as he returned with figures of 15-4-63-0.
Rahul, who made his maiden Test match hundred against Australia at the Sydney Cricket Ground last month, dominated the proceeding early on as Uthappa played second fiddle. Rahul had nine boundaries to his name by the time he reached his half century fifty.
Uthappa reached his first fifty off 116 balls with the help of five boundaries, before amassing the next fifty off just 53 balls.
Brief Scores: Karnataka 302 for 2 (Robin Uthappa 153, KL Rahul 91; Syed Mohammad 1/66) vs Assam.
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