Aparajith was at the crease on 109 along with Dinesh Karthik (11) when the stumps were drawn at the Palam ground here after Tamil Nadu opted to bat first.
Badrinath scored 81 and shared a 168-run stand for the third wicket with 19-year-old Aparajith after hosts Services, last year's semi-finalists, made early in roads into Tamil Nadu's batting.
Yadav, 26, then castled India batsman Murali Vijay (14) to peg the Southern side at 16 for two. Vijay looked promising as he hit three fours in his brief stay at the crease before being dismissed.
The First-class veteran, Badrinath then joined hands with Aparajith to take his side to safety with a century partnership as Services bowlers failed to breach the defences of the two.
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Right-handed Aparajith's 236-ball knock comprised of 12 boundaries while Badrinath took 227 balls for his 81-run innings that included eight fours.
While Yadav finished with figures two for 40 in his 19 overs, Nazar bowled 23 over for 42 to grab the solitary wicket.
Brief Scores:
Tamil Nadu: 220 for three (Baba Badrinath 109 not out, S Badrinath 81; Suraj Yadav 2/40).