Clarke cracked a purposeful 110 to allow Australia to declare on 479 for seven in their first innings on the second day of the Test at the Vivian Richards Cricket Ground.
The Australia vice-captain then returned in the final hour to snare the scalps of opener Xavier Marshall and Runako Morton to leave West Indies wobbling on 125 for three when stumps were drawn.
Clarke took two wickets for seven runs off seven overs. Australia were put on the back foot when Marshall and fellow opener Devon Smith put on 55 for the first wicket.
But Mitchell Johnson made the breakthrough, when Smith was caught at square cover for 16, cutting hard at a short, wide delivery, but straight to the perfectly positioned Andrew Symonds, who nonchalantly grabbed the ball over his head.
Australia continued to bleed runs, and Marshall coasted to his half-century, reaching the landmark when he swung a full toss from leg-spin bowler Stuart MacGill to the fielder on the mid-wicket boundary for a single.
Australia captain Ricky Ponting turned to Clarke for a bit of inspiration, and he deceived Marshall with a well-flighted delivery and the West Indies opener was adjudged lbw for 53 offering no stroke.
Clarke was still celebrating Marshall's scalp, when Runako Morton heaved at another well-flighted ball and was caught at mid-wicket for a five-ball duck to leave West Indies on 105 for three, and captain Ramnaresh Sarwan and Shivnarine Chanderpaul to carry the home team through until the close.
Clarke's fluent batting had propelled Australia into making a declaration at tea, after he reached his landmark, when he drove Daren Powell straight down the ground for the last of his 12 boundaries.
His hundred followed a similar resolute innings of 113 from left-handed opener Simon Katich which had dominated the opening day.
Clarke spent close to four hours 45 minutes at the crease. He shared 72 for the fourth wicket with Katich, added 64 for the sixth wicket with Brad Haddin, and 54 for the seventh wicket with Brett Lee before he was caught at forward square leg off Powell, when he miscued a hook at a short, rising delivery.
Haddin made a handy 33, but Lee blitzed eight fours and one six in 63 from 82 balls and Johnson scored 29 not out to extend Australia's innings to the tea break with an unbroken stand of 65 for the eighth wicket.
Both Aussie lower-order batsmen benefited from sloppy West Indies fielding that saw Fidel Edwards floor Lee on 28 at mid-on off Sammy, the same bowler who suffered when Dwayne Bravo dropped Johnson on 15 at deep extra cover.
But Clarke batted with aplomb from the time he arrived at the crease about 45 minutes before the scheduled close the previous evening.
He stroked the ball with crisp assurance with his classical driving, particularly through the arc between extra cover and mid-off, where he has gathered the majority of his runs.
He'd reached his 50, when he caressed a delivery from Jerome Taylor to mid-off and scrambled a single before lunch.
The innings has been all the more remarkable, considering he arrived in the Caribbean two weeks later than the rest of the squad, after he was granted compassionate leave to attend the funeral of the father of his fiancee.
Clarke had a huge slice of fortune, when wicketkeeper Denesh Ramdin dropped him on 63 down the leg-side, and he made sure West Indies were to rue that miss.
Clarke anchored Australia through the morning period to 360 for five at lunch, although the visitors lost the wickets of century-maker Simon Katich and Andrew Symonds.
Katich was caught down the leg-side, when he feathered his 248th delivery from Taylor in the same over that Clarke reached his half-century.
Symonds arrived and looked set to play in much the same style that he did in the opening Test, but he tried to glance a delivery from Edwards and was also caught down the leg-side for 18.
Haddin joined Clarke and they added 64 either side of lunch before a slower delivery from Taylor deceived him and he was caught at extra cover for 33 to leave Australia 360 for six.
Lee came to crease and they continued to build on the platform of the earlier batsmen, as West Indies wilted under the pressure before a fatigued Clarke lost his wicket.
Jerome Taylor was the most successful West Indies bowler with three for 95 from 27 overs.
Australia lead the three-Test series 1-0, after they completed a 95-run victory in the opening Test last Monday at Sabina Park in Kingston, Jamaica.
Australia have now won 13 of the last 14 Tests they have contested against West Indies and need only a draw to secure their hold on the Frank Worrell Trophy - symbol of Test supremacy against West Indies. The Aussies have not lost a Test series in the Caribbean since 1991.
The third and final Test between the two sides starts on June 12 at Kensington Oval in Barbados.