Smith, who returned to the national set-up earlier this month, posted 76 off 82 balls as Australia chased down 230-run target with more than 11 overs to spare at the Nursery Ground on Wednesday.
The former Australian skipper was out to Carlos Brathwaite with 21 runs still required for victory before Shaun Marsh (55 off 59 balls) and Glenn Maxwell (18 off 12) comfortably guided Australia home.
There was also a injury scare for Australia after Usman Khawaja was struck on his helmet by a steep bouncer from Andre Russell and had to retire hurt. However, Khawaja was cleared of any serious injury after scans revealed that there was no serious damage to his jaw.
Earlier, West Indies recovered from an early collapse of 46/5 and set their opponents 230 to win. Opener Evin Lewis (50 off 56 balls) posted a half-century, while Brathwaite (60 off 64) cracked three sixes in a spirited rearguard late in the innings.
Smith, who had an average run at the recently-concluded edition of the Indian Premier League (IPL), had scored back to back half centuries in warm-up matches against New Zealand XI. He had scored 91* and 89 in the two practice matches and showed signs of him being in full control of his game after serving a one-year ban for his involvement in the Sandpaper Gate.
Head coach Justin Langer has been praising Smith, saying the 29-year-old is in the best physical condition of his life. He, however, said the biggest challenge for both Smith and David Warner in the World Cup would be tackle the England crowd which can be hostile during the showpiece event.
However, England all-rounder Moeen Ali has urged the fans to abstain from making personal comments on Smith and Warner.
"I really hope they don't get too much stick. I want them to enjoy the series. If you have to, keep it funny, not personal," Ali told The Guardian.
"We all make mistakes. We are human beings and we have feelings. I know deep down they are probably really good people. I just hope they get treated decently. I just want the cricket to be spoken about," he added.
Australia will begin their title defense against Afghanistan on June 1 in Bristol.
( With inputs from IANS )