Chasing 289 to win at Trent Bridge, West Indies had half-centuries from Shai Hope (68) and captain Jason Holder (51) but was restricted to 273-9 — mainly because of Mitchell Starc's 5-46, the first five-wicket haul of the tournament.
The Australians, who have also beaten Afghanistan by seven wickets, were only given a decent score to protect courtesy of Steve Smith's 73 and a career-best 92 off 60 balls by Nathan Coulter-Nile. That was the highest score by a No. 8, or lower, in World Cup history.
Australia had been reeling on 38-4 and 79-5.
West Indies opened the tournament with a big win over Pakistan in Nottingham.
Australia joins New Zealand on a maximum four points.
With a patient 54 off 84 balls, Shai Hope was anchoring West Indies' bid to chase down 289 and beat Australia at the Cricket World Cup.
The Windies are 160-4 after 30 overs, needing 129 more runs to win with 120 balls left.
Chris Gayle was given two reprieves by DRS when on 5 before his chaotic innings finally ended on 21. Nicholas Pooran weighed in with a 36-ball 40.
The unbeaten Hope appears to be the key to the reply and is batting in the middle with captain Jason Holder (8).
Nathan Coulter-Nile stroked a career-best 92 off 60 balls after Steve Smith led Australia's recovery from 38-4 as the defending champions reached 288 all out against West Indies at the Cricket World Cup.
Coulter-Nile, a fast bowler, made the highest score by a No. 8 in World Cup history by hitting eight fours and four sixes in an onslaught that jolted West Indies' aggressive pace attack after their superb start at Trent Bridge. His previous best ODI score was 34.
Smith steadied an innings that was rocking at 38-4 and at 79-5 with a 103-ball 73, before he was removed by one of the best catches of the tournament. Sheldon Cottrell took the catch one-handed just inside the boundary, tossed the ball in the air before he went over the rope, and returned to the field of play to collect the ball again.
Pacemen took all 10 wickets, just like when West Indies bounced out Pakistan for 105 last week in a seven-wicket win here in Nottingham.
Australia is also going for a second straight win, having already beaten Afghanistan.
Faced with more aggression from West Indies' pace attack, Australia is in trouble on 48-4 at the end of the opening 10-over powerplay at the Cricket World Cup.
Sheldon Cottrell has been the standout quick for the Windies, removing David Warner (3) and Glenn Maxwell (0) and celebrating his wickets with a military-style salute — a nod to his army background.
Usman Khawaja was roughed up by Oshane Thomas before swatting Andre Russell behind for 13. Aaron Finch was the first batsman to depart, to Thomas, for 6.
Australia is the first team this tournament to lose four wickets in the opening powerplay.
West Indies showed similar aggression in its opening group game against Pakistan, which was bounced out for 105.
West Indies has won the toss and chosen to bowl first against defending champion Australia at the Cricket World Cup.
While Australia's lineup is unchanged from its opening win over Afghanistan, West Indies brought in opener Evin Lewis as a replacement for Darren Bravo in a change to the team that opened with a big win over Pakistan. Shai Hope is likely to drop to No. 3 in the batting order.
Australia captain Aaron Finch said he would have batted first anyway if he'd won the toss, adding that the pitch looked dry and could spin later on.