Andhra, thus, already have a lead of 26 runs with seven wickets to spare in reply to Baroda's first-innings total of 302 all out.
Opener Srikar Bharat top-scored for the hosts with a well-compiled 144 off 301 balls at the Dr PVG Raju ACA Sports Complex.
Bharat struck 21 boundaries and a six.
Ricky Bhui made 90 off 231 balls with the help of seven fours and two sixes.
At stumps on the third day, Bhui and AG Pradeep (33) were the unbeaten batsmen.