Australia replied with 44-0 by stumps with David Warner hitting 27 and fellow left-hander Ed Cowan 13.
Chanderpaul anchored the West Indies from an overnight 179-3 to a satisfying total at Kensington Oval. The 37-year-old left-hander, in his 138th test, struck nine fours and one six in notching his 25th century and fifth against the Aussies. He faced 248 balls and batted for 381 minutes.
Chanderpaul's effort built on earlier half-centuries from Kraigg Brathwaite (57), Kirk Edwards (61) and Darren Bravo (51) and a counter-attacking 41 off 36 balls from captain Darren Sammy.
Part-time legspinner David Warner was Australia's top bowler with 2-45 while Ryan Harris claimed 2-83.
Resuming on 8, Chanderpaul stretched his overnight stand with Bravo to 73 before the Aussies finally struck midway through the morning session.
Bravo hit seven fours and a six off 123 balls before he perished soon after reaching his half-century. The left-hander was caught in the gully as he drove at Shane Watson.
Australia added the scalp of Narsingh Deonarine (21) just before lunch, a lifter from Harris inducing a leading edge that skied to wicketkeeper Matthew Wade to make it 285-5.
Australia should have added Carlton Baugh's wicket before the break but Ricky Ponting couldn't grasp a tough, one-handed effort at second slip off Harris.
Baugh emerged to play some sweet strokes and help Chanderpaul add 31 for the sixth wicket after the break. He was beginning to blossom when he was run out by Harris' direct hit from square leg. The diminutive wicketkeeper made 22.
Sammy provided some impetus with an entertaining cameo that included three fours in one over from offspinner Nathan Lyon and a nasty blow to the helmet after ducking into a bouncer from Watson.
Sammy replied by launching the next ball high over long-off for one of his three sixes. He also hit four fours, dominating a partnership of 53 with Chanderpaul before he miscued to deep midwicket off Ben Hilfenhaus for 369-7.
Chanderpaul received able assistance from the tail as he casually nudged toward three figures.
Kemar Roach took 30 balls in scoring 16 and Fidel Edwards needed 12 deliveries for 10.
But after Roach edged Lyon to slip and Edwards perished irresponsibly by swatting a catch to wide mid-on off Warner, Chanderpaul was still five short with the last man coming in.
Devendra Bishoo proved a sound ally and Chanderpaul raised his century with a pull for two off Hilfenhaus midway through the final session.
Chanderpaul's century took his tally past Viv Richards' 24 among West Indians to now ony trail Brian Lara (34) and Garfield Sobers (26).
The century was also Chanderpaul's fourth at Kensington, the venue where he scored his first back in 1997 against India. During his innings, he also became the leading run-scorer at the ground.
Chanderpaul's only real moment of concern during his typically determined innings was when he survived a close lbw appeal, also denied on the Decision Review System, off Lyon when on 85.
Bishoo finished 18 not out, making it the first time in history that all 11 West Indies batsmen passed double figures, the 12th instance overall.
Australia, left with 45 minutes to bat, responded positively with both openers striking three fours as the West Indies new ball attack of Edwards and Roach were too wayward.