Paliwal and Singh were batting on 106 and 102 at stumps with Services still trailing the hosts by 187 runs. Himachal had made 531 in their first innings.
The two shared a 218-run stand to take the team closer to the opposition total.
Paliwal plundered 13 fours while Singh smashed 16 fours and a six.
Brief scores: Himachal Pradesh 531 all out. Services 344/3 in 122.5 overs (Rajat Paliwal batting 106, Yashpal Singh batting 102).