Sehwag made 284 not out to lift the hosts to 443-1 by stumps on the second day at the Brabourne stadium in reply to Sri Lanka's first innings total of 393.
The Delhi opener had so far hit 40 boundaries and seven sixes in his 239-ball innings, his sixth knock of 200 or more, two of which were converted into triple hundreds.
If he makes 16 more runs on Friday to reach 300, Sehwag will become the first batsman in history to score three triple centuries. Australian legend Don Bradman and West Indian great Brian Lara have two each.
Sehwag made light of the bounce and turn on the Brabourne stadium to share two double-century partnerships during the run-riot, cheered by 15,000 boisterous home fans.
He put on 221 for the first wicket with Murali Vijay (87) and 222 for the unbroken second with Rahul Dravid, whose share in the partnership was 62.
"I missed a big one in the last Test, so did not want to miss out this time," said Sehwag, whose 131 in the second Test in Kanpur last we