Services were comfortably placed when stumps were drawn and are well on course to post a big first innings total at the District Institute of Education and Training Ground here.
Electing to bat, Services lost opener Pratik Desai (14) cheaply but his partner Chatterjee notched up an impressive 103 off 243 balls, which was laced with 15 hits to the fence.
Yashpal's unbeaten knock came off 162 balls and was studded with eight boundaries and a six.
After Desai's early dismissal, one down batsman Anshul Gupta gave Chatterjee company for a while and the duo added 46 runs for the second wicket before the former got out for a well-made 31.
Soumya Swain's (9) stay at the crease was shortlived but his dismissal hardly had any affect on Chatterjee, who went about his business in style and stitched an important partnership of 141 runs for the fourth wicket with Yashpal Singh to take Services forward.
Chatterjee fell in the last session of play.
At stumps, Yashpal Singh was 92 not out and Rajat Paliwal was unbeaten on 23.
For Goa, Saurabh Bandekar bagged two wickets for 74 runs while Amogh Desai and Harshad Gadekar took wicket apiece.
Services: 284 for four in 90 overs (Soumik Chaterjee 103, Yashpal Singh batting 92; Saurabh Bandekar 2/74).