Devin Booker scored 31 points, Chris Paul had 23 and the Suns beat Milwaukee 118-108 on Thursday night to take a 2-0 series lead.
The Suns have never been closer to an NBA title.
Booker made seven 3-pointers and the Suns went 20 for 40 behind the arc. Bridges scored 27 points, and Paul finished with eight assists.
The Suns surged ahead late in the first half, withstood Giannis Antetokounmpo's all-around effort to bring the Bucks back, and walked off winners again as fans swung orange rally towels all around them.
Antetokounmpo had 42 points and 12 rebounds in his second game back after missing two games because of a hyperextended left knee.
The Suns never even had a lead in the NBA Finals until their 118-105 victory in Game 1. They dropped the first two games in both 1976 and 1993, their only other appearances, and didn't win more than two games in either series.
Jrue Holiday played more aggressively but didn't shoot a whole lot better than in Game 1, scoring 17 points but hitting only 7 for 21. Khris Middleton was 5 for 16, forcing Antetokounmpo to carry an even heavier load on his sore left leg.
It adds up to the Bucks having to overcome a 2-0 deficit for the second time this postseason. They did it against the Brooklyn Nets in the Eastern Conference semifinals, but had some help when first James Harden and then Kyrie Irving were injured.
Now they are facing a Suns team loaded with weapons all over the lineup, and showed off all of them in their highlight play.
They whipped the ball all around the perimeter for the final basket of the first half. It went from Paul to Booker to Jae Crowder to Bridges, back to Crowder to Paul, then over to Crowder and once again Bridges. He then finally fed it inside to Ayton, who scored while being fouled with 14.9 seconds left for a 56-45 lead at the break.
The Bucks could only dream of having that many guys involved. Antetokounmpo's 15 field goals were more than twice as many as any other Milwaukee player.
Phoenix opened a 65-50 lead with a good start to the third, but Antetokounmpo - and pretty much only Antetokounmpo - kept the game from getting away from the Bucks. He scored 20 of the Bucks' 33 points in the third, the first 20-point period in the finals since Michael Jordan against the Suns in 1993.
Milwaukee got it all the way down to six in the fourth, but Paul nailed a 3-pointer and Bridges had a basket to quickly push the lead back to double digits.
Milwaukee outscored Phoenix 20-0 in the paint in the first quarter, but eight of the Suns' nine baskets were 3-pointers and they were behind just 29-26.
Only two fouls - both on the Suns - were called in a clean quarter. Antetokounmpo took the only two free throws, making one and shooting an airball on the second as fans continued counting, as they have in Bucks' road games during the playoffs to show that he often doesn't appear to shoot them within the allotted 10 seconds.
It was tied at 41 with just under five minutes left in the half before the Suns surged ahead with precision offense and some shutdown defense. They finished with a 15-4 run, the Bucks managing just a pair of baskets by Antetokounmpo.
He tried to fire up his teammates with some screaming on the bench during a timeout, but he couldn't put the ball into the basket for them. The Bucks were a dismal 6 for 25 in the period, missing 10 of their 12 3-point tries.
Middleton finished with 11 points.