At stumps, Chatterjee was unbeaten on 57 off 115 deliveries while Gupta was batting on the threshold of a half-century.
Chatterjee struck eight boundaries while Gupta hit three fours and two sixes.
Services still trail Himachal Pradesh by 426 runs.
Earlier resuming their first innings at the overnight score of 352 for four, veteran Paras Dogra, who was batting on 174 not out yesterday, completed a fine double hundred.
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Besides Dogra, Nikhil Gangta made 98.
For Services, Diwesh Pathania (3/108) picked up three wickets while Anshul Gupta (2/16) and Vikas Hathwala (2/67) shared four wickets between them.
Brief Scores:
Himachal Pradesh: 531 all out in 138.3 overs (Paras Dogra 227, Nikhil Gangta 98; Diwesh Pathania 3/108).