Brett Lee dismissed Devon Smith for a duck then Shane Warne removed Wavell Hinds for 15 to reduce the tourists to 68 for two in their second innings at stumps on the third day at Adelaide Oval.
That gave the West Indies an overall lead of just 45 runs with two days to go after Hussey blazed an unbeaten 133 to help Australia to finish with 428 and a 23-run advantage on the first innings.
Australia had looked to be in trouble earlier in the day when they slumped to 295-8 after Dwayne Bravo ripped through the middle order before Hussey led his team's fightback.
The left-hander shared a 93-run partnership with Stuart MacGill for the ninth wicket then a 40-run stand with Glenn McGrath for the last wicket.
West Indies made a terrible start to their reply when Smith, who has made just 22 runs in his last five innings after making 88 in Brisbane, was caught by Ricky Ponting at second slip with the total on two.
Hinds was stumped by Adam Gilchrist off Warne shortly before the close of play, leaving Ramnaresh Sarwan and nightwatchman Daren Powell to survive through to stumps.
Sarwan ended the day unbeaten on 53 after reaching his first half-century of the series from 58 balls while Powell had yet to score after being promoted up the order to protect Brian Lara, who made 226 in the first innings to pass Allan Border's world record for the most career runs.
FLAT PITCH
Hussey batted for nearly five hours, faced 215 balls and hit 13 boundaries and three sixes to register his second Test century after making his maiden hundred in Hobart last week.
He was dropped by Sarwan at slip on 88 and by Bravo on 116 when he drove the ball firmly back to the bowler but was otherwise untroubled on a flat pitch.
Hussey is playing in just his third Test and his first as a middle-order batsman after opening the innings in Justin Langer's absence in the first two Tests of the series.
Bravo finished with the impressive figures of six for 84 from 27 overs after dismissing Andrew Symonds, Gilchrist and Warne before lunch then Lee during the middle session after capturing two wickets on Saturday.
Fidel Edwards trapped Brad Hodge lbw for 18 then bowled MacGill for 22 to give him three wickets for the innings while Dwayne Smith bowled McGrath for five to end the innings.
Bravo briefly gave the West Indies some hope of leading on the first innings when he bowled Symonds for nine with a ball that darted back in on the batsman then had Gilchrist caught by Shivnarine Chanderpaul at cover for six after wicketkeeper Denesh Ramdin dropped him on nought.
Bravo took a brilliant one-handed return catch to get rid of Warne for a third-ball duck after having two lbw appeals turned down, then had Lee caught behind for nine when Hussey mounted his recovery mission.
Scorecard
West Indies (1st innings): 405 (B. Lara 226)
Australia (1st innings): (Overnight: 229-3)
J. Langer c Ramdin b Edwards 99
M. Hayden c Chanderpaul b Bravo 47
R. Ponting lbw b Bravo 56
B. Hodge lbw b Edwards 18
M. Hussey not out 91
A. Symonds b Bravo 9
A. Gilchrist c Chanderpaul b Bravo 6
S. Warne c&b Bravo 0
B. Lee c Ramdin b Bravo 9
S. MacGill not out 22
G. McGrath b D Smith 5.
Extras: (lb 7, w 2, nb 15) 24
Total: (all out, 123.3 overs) 428
Fall of wickets: 1-97, 2-211, 3-228, 4-238, 5-271, 6-277, 7-277, 8-295, 9-388, 10-428.
Bowling: Edwards 23-4-114-3 (12nb), Powell 24-6-80-0, Collymore 23-1-59-0, Bravo 27-7-84-6 (2w), DR Smith 17.3-3-59-1, Hinds 9-1-25-0.
West Indies (2nd innings):
W Hinds st Gilchrist b Warne 15
D Smith c Ponting b Lee 0
R Sarwan not out 53
D Powell not out 0
Extras: 0
Total: (for 2 wickets, 21 overs) 68
Fall of wickets: 1-2, 2-60.
Bowling: McGrath 7-2-14-0, Lee 7-1-25-1, Symonds 2-0-9-0, Warne 4-0-17-1, MacGill 1-0-3-0.
