Hayden's hundred, his second in as many matches, was the highest score by an Australian at the World Cup, surpassing the 143 not out made by Andrew Symonds four years ago against Pakistan in Johannesburg.
This innings came after Hayden's 101 in Saturday's 83-run win against South Africa, in what was the first major match at the Sir Vivian Richards Stadium.
It was also the 35-year-old left-handed opener's third hundred in as many one-day internationals against Test nations following his Australian record 181 not out against New Zealand last month in Hamilton.
And yet for all his bludgeoning hitting later on, Hayden struggled at the start of his innings with the Queenslander taking 18 balls to get off the mark.
However, West Indies may take some heart from the fact the four highest totals to win batting second in one-day internationals have all been made against Australia since the 2005/06 season.
Shane Watson was 33 not out and Brad Hogg unbeaten on five.
It was no surprise when West Indies captain Brian Lara decided to field first in overcast conditions on an outfield slowed by early morning rain.
Australia lost Adam Gilchrist for seven when he was caught behind by opposing wicket-keeper Dinesh Ramdin off an inside-edge against Daren Powell.
It was not until the last ball of the seventh over, when captain Ricky Ponting hooked paceman Powell for six, that Australia started to up the rate. Hayden then drove the next two deliveries, from Powell's fellow quick Jerome Taylor, for fours past mid-off.
Ponting had looked in good touch on his way to making 35 off 36 balls before having survived one attempt on 16, ran himself out when he went for a non-existent single off Taylor and Ramnaresh Sarwan at extra-cover hit the stumps at the bowler's end.
Australia, now 76 for two in the 15th over, almost lost Clarke in similar fashion as the innings entered a jittery phase.
And Hayden himself would have been out for 28 if Lara's throw from mid-on had hit after he'd been sent back by Clarke.
Clarke found his form before Hayden reached fifty in typical fashion, advancing down the pitch to drive the off-spin of Chris Gayle, bowling in a cap, down the ground for four.
But a stand of 98 in 16 overs which moved Australia onto 174 for three ended when medium-pacer Dwayne Bravo had Clarke lbw for 41 off just 42 balls.
Hayden completed his ninth one-day international hundred in 110 balls with one six and eight fours.
Hayden then opened up, driving Taylor for six over long-on, lofting him wide of long-off for four and driving him high over long-on again for a six into the upper tier of the stands for three boundaries in as many balls.
Finesse followed force when Hayden late cut Samuels down to third man only for the next ball to be slammed over long-on for six by the Queenslander.
The onslaught was halted briefly when rain, which had been falling steadily, stopped play with Australia 286 for five in the 47th over and Hayden unbeaten on 153.
But the first ball back saw Hayden thrash Corey Collymore for four past the fumbling Dwayne Smith on the long-off boundary before his innings ended when he chipped Bravo to Samuels at long-off having faced 143 balls with four sixes and 14 fours.
Fall of wickets: 1-10 (Gilchrist), 2-76 (Ponting), 3-174 (Clarke), 4-208 (Symonds), 5-234 (Hussey), 6-297 (Hayden)
Did not bat: N Bracken, S Tait, G McGrath
West Indies: Chris Gayle, Shivnarine Chanderpaul, Ramnaresh Sarwan, Marlon Samuels, Brian Lara (capt), Dwayne Bravo, Dwayne Smith, Dinesh Ramdin (wk), Daren Powell, Jerome Taylor, Corey Collymore
Toss: West Indies
Umpires: Aleem Dar (PAK), Asad Rauf (PAK), TV umpire: Billy Bowden (NZL)
Match referee: Chris Broad (ENG)
Reserve umpire: Rudi Koertzen (RSA)