Seeking their first title in their first finals appearance in 28 years, the Suns followed their 118-105 win in Game 1 with a remarkably similar 118-108 victory.
Milwaukee made a far stronger start than in Game 1 and led 29-26 at quarter time, but Phoenix roared into gear to set up the victory with a dominant 30-16 second quarter.
Reigning dual MVP Giannis Antetokounmpo turned in a herculean effort to lead the Bucks with 42 points and 12 rebounds from 40 minutes on court, in only his second game back after a two-match absence with a knee injury.
But he had little support, with Jrue Holiday next best for the visitors with 17 points and Pat Connaughton scoring 14.
Phoenix have already made a better start than in their only previous finals appearance in 1976 and 1993.
Milwaukee can at least hope for improvement in Game 3 on Sunday when the NBA Finals moves to Milwaukee for the first time since 1974.