Syed Sahabuddin struck an unbeaten half century and wicket-keeper Vamsi Krishna (20) and Atchuta Rao (22) showed a lot of determination while batting as they steered the side to a draw at Nehru Stadium.
Starting the day at a precarious 87 for six and trailing by 210 runs, Andhra ended their first innings at 251 all out in 102.1 overs in response to Services' 297.
Right-handed Sahabuddin (78 not out) and Krishna dug in to pull the side out of rut with a 65-run stand for the eighth wicket.
Shadab Nazar broke the partnership by having Krishna caught by Yashpal Singh but Sahabuddin found able allies in Rao and then Rajesh Pawar (17) to take the team past 250-run mark.
Rao was scalped by Suraj Yadav while Pawar fell leg before to Nazar.
In their second essay, Services scored 59 for two in 21 overs after losing both the openers skipper Soomik Chatarjee (1) and Pratik Desai (2) cheaply.
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Anshul Gupta (29) and Yashpal Singh (26) remained unbeaten at the crease.
Brief scores:
Services: 297 and 59 for two (Ansuhl Gupta 29; Duvvarapu Shivkumar 2/8).
Andhra: 251 all out (Syed Sahabuddin 78 not out, Hemal Watekar 45; Suraj Yadav 3/59, Shadab Nazar 3/49).
Points: Services 3, Andhra 1.