Chris Paul and Devin Booker turned on their best form to lead the Phoenix Suns to a 1-0 lead over the Milwaukee Bucks as the NBA Finals series began.

Despite the return from injury of reigning dual MVP Giannis Antetokounmpo for the Bucks, the Suns scored a convincing 118-105 win in Game 1 in Phoenix as they set after their first NBA title.

The 36-year-old Paul made his long-awaited finals debut in style with 32 points and nine assists, while Booker scored 27 points.

Phoenix fans had waited 28 years to see their team in a decider, and the Suns did not disappoint.

They were in front most of the way, leading 30-26 at quarter-time, and by 57-49 at the half.

They then set up the victory with a 35-27 third term in which Paul took control by scoring 16 points, having waited that many seasons to see his first finals action.

Deandre Ayton scored 22 points and had a major impact in defence with 19 rebounds, while Mikal Bridges scored 14.

Antetokounmpo, having missed the last two games with a knee injury, led Milwaukee with 20 points and 17 rebounds, while Khris Middleton had 28 points and Brook Lopez 17.

The Bucks will again have to come from behind, having now lost Game 1 for a third straight series.

Paul said he was pleased to have improved his shooting in the third quarter and indicated the Suns were intent on working on their pacing of matches through the series.

"I got my head in the game, I saw the shots they were giving me and I was just missing them, so I just kept trying to be aggressive and my guys got going," he told ESPN.

"The coaches were talking about pace, I'm the old head that likes to slow it down sometimes but in this series we've got to play with pace."

Game 2 is in Phoenix on Thursday night.