Shaikh, playing his third First-class match, remained unbeaten on 118 at stumps alongside Rahul Tripathi (19*).
The other major contribution came from Ankit Bawne, who scored 83.
Veteran pacer Pankaj Singh was the pick of the Rajasthan bowlers, taking two wickets for 38 runs.
Shaikh played 258 balls in his gritty innings, collecting 18 fours and a six.
Bawne, who was dismissed in the 70th over, gave good support to Shaikh as the duo shared a 177-run partnership for the third wicket.