At the break, Australia, leading by 127 runs from the first innings, reached 92 for one in their second innings with Phil Jaques not out on 33 and Ricky Ponting not out on 13 on the fourth day of the Test at the Vivian Richards Cricket Ground.
Australia lost makeshift opener Mike Hussey before the break, when he was caught behind driving loosely at a delivery from Dwayne Bravo.
Hussey was promoted to open the batting, after Simon Katich was forced to seek medical treatment for a bruised rib which he sustained when he scored 113 in the first innings.
Lee had captured five wickets for 59 runs from 21 overs, as West Indies, replying to Australia's first innings total of 479 for seven declared, were dismissed for 352 about 10 minutes before the scheduled lunch interval.
It was the ninth time in a Test that Lee had taken five wickets or more in an innings, and sent West Indies crashing from the comfort of 314 for four to transform the complexion of the match.
Lee triggered a collapse which saw West Indies lose their last six wickets for 38 runs in the space of 68 balls.
His bowling completely overshadowed another epic Test hundred from long-standing West Indies left-hander Shivnarine Chanderpaul, whose undefeated 107 was his 19th Test hundred and second in successive matches.
Chanderpaul reached his milestone, when he swept Andrew Symonds for the 11th of his 12 boundaries from 236 balls in almost six hours of batting.
Australia had been kept at bay for close to an hour-and-a-half by Chanderpaul and Bravo in a stand of 132 for the fifth wicket before Lee made his presence felt with five wickets for five runs in the space of 18 balls.
The Aussie fast bowler started the rout, when he had Bravo dubiously caught down the leg-side for 45, although television replays suggested umpire Russell Tiffin may have erred with his verdict as the ball appeared to have ricocheted from the batsman's thigh pad.
This dismissal seemed to have energised Lee getting a ball more than 90 overs old to reverse swing on a hard, docile pitch in hot, sunny conditions.
Next delivery, Lee gained another dubious decision from Tiffin to have Denesh Ramdin adjudged lbw for a first-ball duck to a delivery which moved back from outside the off-stump, but which TV replays suggested its flight path was hardly threatening.
In his next over, Lee also gained another marginal lbw decision from Tiffin to send Darren Sammy back for a second-ball duck.
Lee then ended a late flourish of 20 from Jerome Taylor which included two fours and a six from 26 balls, when he bowled the West Indies fast bowler, and completed his landmark, when he gained a third, but palpable lbw verdict to dismiss Daren Powell for a two-ball duck.
Mitchell Johnson swiftly ended the West Indies' innings, when he had Fidel Edwards caught behind for a 10-ball duck in the next over.
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 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.