Sent in to bat for the fourth straight time after losing every toss of the coin, West Indies made 9-205 at Warner Park in Basseterre, St Kitts on Saturday night.
No overs were lost despite a 55-minute rain break with four balls of the West Indies innings left.
The Australian catching was exceptional, with Maxwell going low and leaping high to take two excellent efforts at mid-off, and Mitchell Owen taking a diving snare at deep backward point.
Maxwell's athleticism shone again late in the innings, when he took a high catch at long-on and flicked the ball back to Cameron Green before falling over the boundary to complete the dismissal.
The innings was full of brief explosive batting cameos, with Sherfane Rutherford (31 off 15), Romario Shepherd (28 off 18), Rovman Powell (28 off 22), Jason Holder (26 off 16), Shimron Hetmyer (16 off 6) and Matthew Forde (15 off 7) all unable to capitalise on fast starts.
Australia made two changes to the team with game three centurion Tim David and paceman Ben Dwarshuis rested, replaced by allrounder Aaron Hardie and paceman Xavier Bartlett.
The two inclusions bowled the opening five overs of the innings and combined to take the first wicket, with Brandon King caught at mid-on by Hardie off Bartlett's last ball of his first over.
Bartlett (2-39 off 4) struck again with the first delivery of his next over, having West Indies captain Shai Hope caught at mid-on by Maxwell.
Maxwell's second catch removed Roston Chase for a first-ball duck off Hardie.
Wickets fell at regular intervals, but West Indies maintained a strong run-rate, smashing 21 fours and 12 sixes.
Nathan Ellis (0-21off 4) and Hardie (2-24 off 4) both bowled tidily on a small ground with short boundaries.
Paceman Sean Abbott (2-61 off 4) and legspinner Adam Zampa (3-54 off 4) bore the brunt of the assault.
