Chris Paul called the tune in Game 1 of the NBA Finals on Tuesday, with the Phoenix Suns point guard orchestrating a 118-105 triumph over the Milwaukee Bucks.

Making his first finals appearance in year 16 of his stellar career, Paul led the way for the Suns with 32 points as they capitalised on home advantage to take an early lead in the best-of-seven series.

Devin Booker contributed 27 and Deandre Ayton produced yet another playoff double-double, the center collecting 19 rebounds to go alongside his 22-point haul.

However, in a contest that saw Giannis Antetokounmpo make his return from injury for the Bucks, it was Paul who stole the show - including making six of his seven attempts in a third-quarter push.

"When it's going like that, you just want to space the floor well and let him orchestrate," Suns head coach Monty Williams said about Paul's third-quarter performance, which also included a trio of successful three-pointers.

"I thought he was making the right plays. They were switching a ton, and we have to offer that space and play faster if he gets off of the ball.

"But he was making shots and when he's in that mode, we just feed off of that.

"I don't have a marker or a segment in the game where I'm like, here he goes. It just happens. Our guys feed off of those moments in the game."

The Suns - back in the NBA Finals for the first time since 1993 - had benefited from some extra rest ahead of the series, having clinched the Western Conference title with a 4-2 triumph over the Los Angeles Clippers at the end of June.

In contrast, the Bucks' battle with the Atlanta Hawks only came to a conclusion on Saturday.

"It's the formula for any team. You want to win every game, but especially the first game it gives you a level of confidence," Williams told the media. 

"Our starts over the course of the playoffs, when we start well, it tends to build confidence for our team.

"I think about Game 5 against the Clippers when we had that below-average start. We were digging ourselves out of a hole. And it wasn't just the offense. It was just having the energy and the juice that we typically play with. So I do think it's important.

"I think our guys understand that and we need to do it every time we step on the floor."

Back in action after hurting his left knee in Game 4 against the Hawks, Antetokounmpo had 20 points and 17 rebounds for Milwaukee in a losing cause. 

Khris Middleton led the way for the Bucks with 29 points, but for a third straight series Mike Budenholzer's team have lost Game 1.