Ellis made his final two points from the foul line with 16 seconds left to give the Bucks a six-point lead and they went on to win for the fourth time in six games.
Phoenix had won each of the last 24 times Milwaukee had come to town, including all 19 that had been played at US Airways Center -- a building that opened in 2991.
Ellis was supported by a career-best 19 points and 15 rebounds from Larry Sanders. Brandon Jennings and Mike Dunleavy had 16 points each for the Bucks, who put together a 10-point run after falling behind by two with 4 minutes to go.
2014: The Year in Music [PHOTOS]