Australia 314 for 7 (Peake 109, Samuel 56, Pollard 2-37, Gittens 2-45) beat West Indies 292 for 9 (Carter 64, Dorne 62, Lachmund 4-66, Aryan 2-47) by 22 runs
After being put into bat, Will Malajczuk gave Australia a fast start with a 30-ball 48.
Nitesh Samuel, his partner, played his part by scoring 56 off 74 and being part of 50-plus stands for the opening and third wickets.
Peake, who came in after 11 overs at No. 4, batted for the rest of the innings, across 166 minutes, for his 109 off 117 balls. Aside from Samuel, he found Alex Lee Young (45 off 47) and Jayden Draper (29 off 23 balls) for company.
R'Jai Gittens took two key wickets at the top including that of Malajczuk.
Jakeem Pollard, with 2 for 37, was the most economical bowler and had the best figures for West Indies.
West Indies got off to a strong start and were in front for the first half of the chase. It started with an 88-run opening stand between
Zachary Carter and Tanez Francis followed by a brisk 35-run partnership between Carter and Jewel Andrew.
Carter's 42-ball 64 and Andrew's 38-ball 44 were followed by a half-century from captain Joshua Dorne at No. 4 but his 62 took 97 balls. All of West Indies' top-six batters scored more than 25 each but they unraveled in the final ten overs when they needed 83 to win with seven wickets in hand. But they went on to lose for 5 for 52 while trying to get close to the target.
Lachmund was the chief destroyer taking 4 for 66 in his nine overs. Hayden Schiller and Aryan Sharma took two wickets apiece while Naden Cooray took the key wicket of Carter and gave away just 38 off his ten overs.