Standing in for injured regular skipper Mahendra Singh Dhoni, Kohli scored 115 to help push the tourists within 148 runs of Australia's first innings total of 517-7, with the hosts declaring before the start of play at Adelaide Oval.
Paceman Mitchell Johnson struck Kohli on the helmet first ball and ended up dismissing him late in the day when the batsman miscued a pull shot to deep fine leg where Ryan Harris charged in to take a fine, low catch.
Wicketkeeper Wriddhiman Saha (one not out) rode out a tense few overs to stumps, with middle order batsman Rohit Sharma on 33.
After India were largely dominated on the field, Kohli's wicket left the test evenly poised, according to Australia spinner Nathan Lyon, who bowled well for his two wickets.
"It's pretty even-stevens, really," he told state radio ABC.
"They batted well but they're still five down and we've still got a lead of 140 or so. So if we come out and bowl well tomorrow, hopefully we can get a good solid lead."
Lyon removed Ajinkya Rahane for 62 in the last session for his second wicket but all of India's top order batsmen made positive starts on a day of bright sunshine.
Only 26-year-old Kohli really cashed in, however.
He was hit first ball by a searing bouncer from Johnson which struck him flush on the badge of his helmet, but he responded by spanking the paceman to all corners of the ground in the final session before eventually holing out.
With the death of Phillip Hughes from a bouncer still fresh in all minds, the Australians rushed to the batsman out of concern and Clarke consoled Johnson as he walked back to his mark visibly distressed.
Kohli brought up his ton with a well-struck four steered through midwicket and after ripping off his helmet, yelled "Come on!" at the India team box, eyes blazing.
Lyon broke a 101-run partnership between Kohli and Rahane with an unplayable ball that reared out of a rough patch and pinged off the middle order batsman's glove to fall to Shane Watson at slip.
Lyon also ended an 81-run stand between Kohli and Cheteshwar Pujara with a ball that dribbled through the number three's legs and onto the stumps.
Left-armer Johnson was punished for some wayward bowling but teased a nick from opener Murali Vijay into the slips to have him out for 53 just before lunch.
Seamer Ryan Harris, back in the side after a long recovery following knee surgery, bowled opener Shikhar Dhawan who had raced to 25 before edging on to the stumps.
Australia captain Michael Clarke took to the field after battling through back pain to score his courageous 128 on day two, but was clearly restricted in his movement and sluggish to chase down balls.
