At stumps, HP were 98 for one in their second essay with Varun Sharma batting on 35 and Paras Dogra on 41.
HP still trail Maharashtra by 162 runs with nine wickets in hand and a full day's play remaining.
Earlier in the day, Bawne completed a fine century after resuming at his overnight score of 76.
Apart from Bawne, Shrikant Mundhe (58) scored a half-century off 96 balls which was studded with nine boundaries and one six.
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Akshay Darekar remained unbeaten on 34 off 46 balls along with Bawane, but Chirag Khurana (43) departed after just adding six runs to his overnight score.
For HP, Vikramjeet Malik (2/71) and Rishi Dhawan (2/131) shared four wickets between them.
Brief Scores:
Himachal Pradesh: 228 & 98 for one in 40 overs (Paras Dogra 41 batting, Varun Sharma 35 batting; Anupam Sanklecha 1/22).
Maharashtra: 488 for six decl in 145 overs (Ankit Bawane 138 batting, Harshad Khadiwale 92, Shrikant Mundhe 58; Vikramjeet Malik 2/71).