A counterattacking 157 from Rajat Paliwal and his 197-run fourth-wicket stand with Yashpal Singh notwithstanding, Services were unable to avoid the follow-on.
Sent in again, they slipped to 122 for 6 by stumps at Conor Vayal Stadium at Tellicherry.
They were 53 for 6 at one stage, before Nakul Verma (25 batting) and the aggressive Saurabh Kumar (41 batting) dragged the score into three figures and the match into the final day.
Leg-spinner Amit Verma took two wickets on the second evening and three at the end of Services' first-innings to claim his second five-for on the bounce, after his 5/61 against Tripura.