Dogra, overnight unbeaten on 21, finished unbeaten on 209 off 241 balls with the help of 23 boundaries and six hits over the fence as Himachal Pradesh declared their first innings at 561 for five in reply to Tripura's 285.
Apart from Dogra, Robin Bist made 58 while Nikhil Gangta scored 50.
Besides, Himchal Pradesh openers Ankush Bains (114) and Prashant Chopta (101) too struck centuries yesterday.
Tripura were 88 for three in 30 overs in their second innings.
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The visitors still need to amass 188 runs to avoid an innings defeat, which looks highly unlikely with one full day's play remaining in the match.
Udiyan Bose was unbeaten 29, while giving him company was Rakesh Solanki on 5.
Ankush Bedi picked (3/37) up all the three Tripura Pradesh wickets.
Brief Scores:
Tripura: 285 & 88 for three in 30 overs (Udiyan Bose 29 not out; Ankush Bedi 3/37).
Himachal Pradesh: 561 for five decl in 130 overs (Paras Dogra 209 not out, Ankush Bains 114, Prashant Chopra 101; Rana Dutta 3/79).