West Indies finished the day on 71 for five in its' second innings, leading by just 114 runs after Australia's tail wagged and Hilfenhaus knocked over their top order yesterday.
Earlier captain Michael Clarke declared Australia's first innings at 406 for nine with his side still trailing by 43 runs. It was an aggressive move allowing his bowlers to attack the West Indian batsmen either side of tea and Hilfenhaus took advantage in the 25 minutes leading up to the break removing the top three.
Harris - who had earlier hit an unbeaten 68 - added the important scalp of Shivnarine Chanderpaul shortly after tea.
It was a remarkable turnaround in fortunes as the Australians had at one point been 199 runs behind with only three first innings wickets remaining. It looked as though the West Indies would have a commanding first innings lead when, just as they had on the third day, they broke through early on. In the fourth over Mike Hussey drove at a ball from Kemar Roach that found the edge and Carlton Baugh dived across in front of first slip to claim the key wicket.
Peter Siddle started to duck the second ball that he received from Fidel Edwards but it didn't climb as high as he'd anticipated. As he adjusted the ball looped off the bat where Kirk Edwards took another fine catch in the gully.
Australia had lost two wickets for two runs. Harris played positively from the start of his innings as he and Matthew Wade added 35 runs for the eighth wicket. The Australian 'keeper fell for 28 in his first Test innings when he took a wild drive at a wide Fidel Edwards ball that Darren Bravo took easily at second slip.
Harris and Hilfenhaus played gutsy innings as they gradually reduced the deficit with Harris passing his top score in Test cricket, made in his last innings against India in Adelaide.
The ninth wicket partnership of 44 was finally broken when Hilfenhaus, on 24, played an extravagant shot across the line and Roach's delivery took out the middle stump.
The West Indies still had a 120 run lead when last man Nathan Lyon came to the crease but the last pair frustrated the home team and played so well that Lyon hit his highest first class score of 40.
They had added 76 runs when Clarke decided to declare. It proved to be a brilliant move as Hilfenhaus took out the top three batsmen.
Barath was comprehensively bowled through the gate for two and two balls later Kraigg Brathwaite, who had played such a patient innings first time around, had an uncharacteristic go at a wide delivery and Wade took the catch.
There was more drama in the next over. Shane Watson opened the bowling with Harris still off the field after his batting efforts and almost removed Kirk Edwards but Ricky Ponting's wonderful effort was judged to have hit the turf just before he caught it at second slip.
However, Edwards in the next over moved across his stumps to another Hilfenhaus delivery and was given out lbw that was confirmed after the West Indies reviewed the decision.
When Harris returned to the bowling he struck a major blow when he bowled the perfect line to Shivnarine Chanderpaul who edged through to Wade to leave the West Indies reeling at 17 for four.
Darren Bravo and Narsingh Deonarine steadied things as they added fifty for the fifth wicket. A tight spell by Siddle eventually drew Bravo into a loose shot outside of the off stump when he'd scored 32 and he was caught behind.
West Indies (1st innings ) 449 for 9 declared
Australia (1st innings) (248 for 5 overnight)
E. Cowan c Baugh b Sammy 14
D. Warner c Bravo b Sammy 42
S. Watson c Baugh b Roach 39
R. Ponting run out (Brathwaite/Baugh) 4
M. Clarke c Deonarine b Bishoo 73
M. Hussey c Baugh b Roach 48
M. Wade c Bravo b F. Edwards 28
P. Siddle c K. Edwards b
F. Edwards 0 R.
Harris not out 68
B. Hilfenhaus b Roach 24
N. Lyon not out 40
Extras (LB-13, W-5, NB-5) 26
Total: (declared 9 wickets for, 145 overs) 406
Fall of wickets: 1-50, 2-65, 3-83, 4-133, 5-215, 6-249, 7-250, 8-285, 9-329. Bowling: F. Edwards 31-4-92-2, Roach 29-8-72-3, Bishoo 45-10-125-1, Sammy 21-6-65-2, Deonarine 19-5-36-0.
West Indies (2nd innings)
A. Barath b Hilfenhaus 2
K. Brathwaite c Wade b Hilfenhaus 0
K. Edwards lbw b Hilfenhaus 1
D. Bravo c Wade b Siddle 32
S. Chanderpaul c Wade b Harris 12
N. Deonarine not out 20
C. Baugh not out 2
Extras (LB-1, NB-1) 2
Total: (5 wickets, 38 overs) 71
Fall of wickets: 1-2, 2-3, 3-4, 4-17, 5-67. Bowling: Hilfenhaus 10-4-17-3, Watson 6-1-16-0, Harris 3-1-14-1 (1nb), Siddle 9-2-11-1, Lyon 9-4-10-0, Clarke 1-0-2-0.