Bevan hit 59 not out to lift Australia to 189 for 9 in their 50 overs after they had been in deep trouble at 104 for 8. West Indies then contrived their own downfall as three of their top four batsmen were run out and they were all out for 169 in 46.2 overs.
Mervyn Dillon's burst of four wickets for two runs in five overs destroyed Australia's middle order, but Bevan halted the collapse with a fighting innings and, with Shane Warne, set an Australian one-day international ninth-wicket record partnership of 77.
West Indies began their reply well, but had the opener Ridley Jacobs and Jimmy Adams run out. Lara pulled one powerful boundary off Warne but then the leg-spinner bowled him for six. West Indies' hopes lay largely then with Carl Hooper but he also went for an unnecessary run and fell Ricky Ponting's accurate throw for 23.
On Saturday, a century partnership between Sherwin Campbell and Adams had set up West Indies for a five-wicket victory. The visitors, who won the toss, scored 242 for 7, but then lost their main strike bowler, Glenn McGrath, to injury. They were always struggling to restrict West Indies after McGrath limped from the field after one over, having turned his left ankle when he slipped in the field. West Indies reached 244 for 5 with six balls to spare.