Laxman, on 104 not out, has belted 10 fours during his fine 174-ball knock while opener Gautam Gambhir was going strong on 191 as the hosts seized the initiative in the crucial tie.
India lead the four-Test Border-Gavaskar series 1-0 after winning the previous match in Mohali by 320 runs. The opener in Bangalore ended in a draw.
Gambhir, 149 overnight, continued to play the anchor role to perfection, putting on 236 runs for the unbroken fourth wicket with Laxman, who notched up his 13th Test century.
The stylish Laxman was stuck for 11 balls on 99 but reached the coveted mark with a cover-driven four off leg-spinner Cameron White, who conceded 52 runs off his 10 overs.
Gambhir, who shared a vital stand of 130 with Sachin Tendulkar (68) to pull India out of trouble after they were reeling at 27-2, has so far belted 24 fours and a six in his 362-ball knock.
Laxman, who has a knack of playing big innings against Australia, and Gambhir denied the tourists any success in the morning session, putting on 97 runs off 26 overs after resuming on 296-3.
Australian pace spearhead Brett Lee (1-92) bowled with purpose and intent and was unlucky after Laxman fended off a rising ball clumsily.
Other than that scare, Laxman -- one short of playing his 100th Test -- used his wrists beautifully to pull and drive the bowlers on both sides of the wicket.
Gambhir continued to mix caution with aggression and looked set for his first double-century.
He offered a chance when on 176 but his edge off leg-spinner Cameron White evaded Matthew Hayden in the slips.
The fourth and final Test is slated to be played in Nagpur from Nov 6-10.