AUSTRALIA won an exciting first Test against West Indies by three wickets in Barbados as Michael Clarke’s team were rewarded for their positive approach.After West Indies were bowled out for 148 before lunch on the final day in Bridgetown, the tourists were set a victory targer of 192 in two sessions.Australia were cautious before tea but with the light fading fast, they stepped up the run-rate in the final session despite losing six wickets in the process.Spinner Narsingh Deonarine took 4-53 as West Indies exposed the Australia tail but with Mike Hussey (32) taking an aggressive approach, Australia were able to cross the finish line before darkness fell.The victory completed an outstanding turnaround from the tourists who at one stage in their first innings were 250 for seven chasing 449 for nine declared before Ryan Harris and the tail produced invaluable resistance."It was very hard fought. Australian cricket has very fond memories of this ground in Barbados and I think the last five days will be added to those great memories,” said Clarke, who was part of the team which won the World Cup at Kensington Oval in 2007.Clarke’s decision to declare Australia’s first innings on Tuesday at 406 for nine, even though they were 43 runs behind, proved to be a master-stroke, exposing a seemingly tired unprepared West Indies top order to a tough afternoon session.Clarke said: "I think you have to give yourself every opportunity to win. I think full credit has to go to our bowlers, not only the way they batted in the first innings but the way they came out and bowled in the second innings as well. That went a long way to helping us win the game.”Man of the match Harris finished with three for 31 to follow up on Tuesday’s batting heroics - he got the first breakthrough of the day trapping Deonarine (21) leg before.West Indies, needing to eat up time and add runs, really needed a strong contribution from skipper Darren Sammy but he made just 14 before he was bowled by Shane Watson.Harris then proved his worth in the field with a catch at mid-on when Carlton Baugh (23) attempted to drive Ben Hilfenhaus (4-27).