The hosts then reduced Goa to 72 for one at stumps.
After resuming on 240 for five, Muzumdar, starting on 56, and Shivkumar on 12, gave an ideal start to their team.
Shivkumar and Muzumdar shared a valuable 124-run partnership for the sixth wicket to take their team past 300-run mark.
Muzumdar added 32 runs to his overnight score before he got out for 88 off 186 balls, laced with 11 hits to the fence.
After Muzumdar's dismissal, Shivkumar continued to play with shots in the company of the tailenders.
While Shaik Basha (10) and T Vamsi Krishna (16) sustained for a while but soon Shivkumar ran out of partners to remain stranded at 195-ball 106, studded with 12 fours and a six.
Replying to Andhra's huge first innings score, Goa lost the wicket of Swapnil Asnodkar (13).
At stumps, Sagun Kamat was batting on 41, while giving him company at the other end was AS Desai on 12.
Brief scores:
Andhra 1st inngs: 393 all out in 137.1 overs (Duvvarapu Shivkumar not out 106, Amol Muzumdar 88; Saurabh Bandekar 5/107, HH Gadekar 4/97).
Goa 1st inngs: 72 for one in 31 overs (Sagun Kamat batting 41; Duvvarapu Shivkumar 1/06).
