Ellis scored 27 points and handed out 13 assists, Ersan Ilyasova added 20 points and the Bucks won in Houston for the second straight season.
The Bucks went down to the wire again after beating Dallas 95-90 on Tuesday and losing their previous three games by no more than three points. Ellis took a pass from Brandon Jennings and heaved a shot off one foot as time was winding down. The referees watched a replay and ruled that Ellis shot it in time.
James Harden scored 25 and Omer Asik grabbed a career-high 22 rebounds for Houston.
Larry Sanders tipped in an Ellis miss to put Milwaukee up 107-105. Harden answered with a driving layup to forge the game's 11th tie. Ellis rebounded an Ilyasova miss with 23 seconds left to give the Bucks one more chance to win it in regulation.
Mike Dunleavy had 16 points and new acquisition J.J. Redick added 14 for Milwaukee. Chandler Parsons scored 20 and Donatas Motiejunas added 13 in his first start for Houston. Jeremy Lin had 10 points on 4-of-11 shooting.
Motiejunas hit his first shot, a 3-pointer from the corner, during Houston's opening 28-11 spurt. The 7-foot Motiejunas, a first-round draft pick in 2011, had three stints in the developmental league this season and was last recalled on Jan. 28.
The Rockets made 12 of their first 13 shots and Lin had one of the early highlights, spinning a behind-the-back pass to Parsons for an easy dunk. Houston had 10 assists on its first 12 baskets, but after Asik finished an alley-oop from Parsons with a dunk, Houston went scoreless for almost three minutes.
Jennings hit consecutive 3s and Mike Dunleavy scored on three layups as Milwaukee mounted a 21-6 run to cut the deficit to two. The Rockets struggled to regain their offensive flow in the second quarter, missing 12 of their first 17 shots. Ilyasova sank a long jumper and Ellis added two free throws in the last minute before the break to tie it at 55-all.
Harden played with a wrap on his left knee after he bumped into Ellis in the first half. Ellis, coming off a 22-point game in Dallas on Tuesday night, scored seven points early in the third quarter to help Milwaukee build a seven-point lead. The Rockets quickly rallied, and Asik completed a three-point play to put Houston ahead 70-68 with five minutes left in the third quarter.
Dunleavy twisted his right ankle in the last minute of the third quarter and hobbled to the locker room. He returned with just under 10 minutes left in the game and the Rockets leading 88-84.
Houston continued to misfire from 3-point range early in the final quarter and Redick's 3-pointer near the six-minute mark put Milwaukee up 99-96. Backup Houston point guard Patrick Beverley answered with a 3 to forge the ninth tie of the game.
NOTES: Bucks C Ekpe Udoh sprained his right ankle in the first quarter and did not return. ... Ellis had six steals and leads the NBA with eight games this season with at least five steals. ... Rookie Thomas Robinson, acquired in a trade with Sacramento last week, had a basket, a rebound, an assist and three fouls in his Houston debut. ... The Rockets have won 10 of the last 13 meetings with the Bucks. ... Asik has 26 double-doubles and 39 games with double-digit rebounds this season.