Dogra scored a brilliant 121 off 183 balls, studded with 18 fours and three sixes to help the hosts take a 21-run first innings lead with six wickets remaining.
At stumps on day two, Amit Kumar was unbeaten on 18, while Aatish Bhalaik was yet to open his account.
Resuming at 196 for eight, Kerala's overnight unbeaten centurion Sanju Samson continued with his good work before he ran out of partners at the other end to be left stranded at 127 not out.
Another overnight batsman, Prasanth Parameswaran, who resumed on 13, could add only four more runs before Vikramjeet Malik sent him packing, adding third wicket to his kitty.
The last batsman -- KR Sreejith -- got run out for nought.
For Himachal, Malik (3/47) and Rishi Dhawan (3/77) claimed three wickets each, while Gurvinder Singh took two for 47 and Mohinderraj Sharma claimed one for 50.
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Replying to Kerala's modest total, Himachal lost Prashant Chopra for a quickfire 24. Thereafter, Aakash Chopra (18) and Dogra put on a 78-run stand together for the second wicket.
After Aakash Chopra's departure, C Hemanth Kumar (45) also chipped in with crucial runs.
In another Group C match at Jammu, Jharkhand took a massive 159-run lead over Jammu & Kashmir after posting 354 for eight in their first innings on the second day of the match. MORE