"This is as good as I've had, no doubt, because we had our backs to the wall for the first three days of the game," said Clarke, putting the win above his inaugural test victory on a dustbowl in Sri Lanka or the dramatic two-wicket victory over South Africa in November.
"The spirit and the character ... of the guys in the change room is what drives you, I guess, as a captain to make a bold decision, to declare when I declared.
"The confidence around me from everybody in that group, there wasn't one bit of fear of losing that test match - it wasn't spoken about.
"From day one of the test, all that's been spoken about is what we have to do to win this test match."
Man-of-the-match Harris, promoted above Peter Siddle in the second innings, admitted to having to make a dash from the toilet to pad up as Australia's run chase began to falter on a dying fifth-day wicket.
Offspinner Narsingh Deonarine claimed 4-26 in a withering spell into the rough after tea before paceman Kemar Roach ended the innings of debutant Matthew Wade (18) and Michael Hussey (32) to put jitters through Australia's chase.
In the end, though, Hilfenhaus - who took 4-27 in the Windies' second-innings 148 - sealed the victory, celebrating with Harris even as the third umpire ruled him not out on a run-out appeal.
"I actually said to Mike Hussey before tea that I'd love to be out there at the end of a test match and hit the winning runs," Harris said.
"I didn't do that but I was out there. It was a good feeling. To win it after them making 450 and being in a position where the game washeading to a draw, that's a huge win for us."
The second test in the series begins in Trinidad on Monday.
- AAP
