Responding to Serives' 226 in the four-day encounter, the Bipul Sharma-led Himachal finished Monday on 255 for six - a lead of 29 runs.
Starting the day on 19 for no loss, wicketkeeper-batsman Bains (67) struck a 101-run opening stand with Raghav Dhawan (38) to the team a solid start.
A bit of a stutter in the middle but Parida (54 not out) soon stabilised the boat by registering his 48th first-class fifty and stayed on till stumps, with Nikhil Gangta (10 not out) giving him company.
Brief Scores:
Services 226 in 80.1 overs (Deepak Punia 64, Saumik Chatterjee 42; Vikramjit Malik 3/57. Rishi Dhawan 3-57)
Himachal Pradesh 255/6 in 97 overs (Ankush Bains 67, Rashmi Parida 54 not out, Nikhil Gangta 10 not out; Suraj Yadav 2-55, Abhishek Sakuja 2-30).