Smith (192) completed his highest career score ??? and third hundred of the series ??? before falling just short of a maiden double ton, while Harris (74) smacked eight fours and a six in a thrilling 88-ball stay at the crease as the hosts moved from 259-5 overnight to 503 all out.
Harris and Smith then combined to remove Shikhar Dhawan (28) before India, already 2-0 down in the four-match series, grafted their way to 108-1 at stumps, 422 runs in arrears.
Smith ??? who now averages 189 in the series ??? began day two on 72 and quickly chalked up his fifth ton of 2014, with the milestone coming off 191 deliveries.
Brad Haddin (55) gave his skipper ample support, recording his first Test fifty since scoring 75 against England in last year???s fifth Ashes encounter in Sydney, but returned to the pavilion when he bottom-edged ??Mohammed Shami through to MS Dhoni.
However, Mitchell Johnson ??? who gave a glittering example of his batting skills when he crunched 88 off 93 balls in Australia???s second Test victory in Brisbane ??? hit five fours en route to an eye-catching 28 before he was snaffled by R Ashwin.
Harris, though, played the aggressor in his 106-run stand with Smith for the eighth wicket, passing his previous best Test total of 55 against England at Adelaide in 2013 courtesy of some hefty blows.
The 35-year-old was eventually trapped lbw by Ashwin, Nathan Lyon (11) became Shami???s fourth victim of the innings when he was castled, and then Smith???s hunt for his double hundred was ended when his poles were rearranged by Umesh Yadav.
The captain was given a rousing reception as he strolled off the field and delighted the Australia fans further when he took a diving catch at second slip to dislodge Dhawan after the India opener had fended at a Harris delivery with the score on 55.
The Baggy Greens could have had another breakthrough but Haddin dropped Cheteshwar Pujara on 12, and the Indian No 3 (25 not out) and opener Murali Vijay (55 not out) held firm until the end of the day.