Ellis hit a jumper with 17.3 seconds left to put the Warriors up by four. He scored 24 points to lead Golden State.
Corey Maggette scored 12 of his 21 points in the fourth quarter for the Bucks.
Luc Mbah a Moute had a career-high 19 rebounds and a season-high 15 points. Ersan Ilyasova had 23 points, two off his career high, and 13 rebounds.
Milwaukee took a 73-72 lead into the final quarter.
The lead changed hands 12 times in the second quarter, including 11 of the final 13 made baskets, with the Bucks taking a 47-46 edge into the intermission.