Tobias Harris scored 18 points for Milwaukee and Ellis had 14.
The Bucks led 94-72, matching their biggest lead, on a basket by Jennings with 3:45 to go in the game before the Celtics whittled the final margin to 11 points.
The Celtics have just six players who saw action with the team last season and are struggling defensively after holding opponents to the lowest field goal percentage in the league, 41.9 percent. Offensively, the Celtics could do little inside.
"We locked down that paint pretty good," said Larry Sanders, who had 10 points and seven rebounds for the Bucks. "We were all dependent on our teammates."
The Celtics allowed the Heat to shoot 54.4 percent in the opener and the Bucks to make 46.5 percent. In their final regular season game last season, the Celtics beat the Bucks 87-74.
"We missed the playoffs two years in a row, so it started from tonight," Jennings said. "Whether I shoot bad or not, just as long as they know I gave it my all."
Milwaukee took control after Paul Pierce gave Boston its last lead, 10-8, with two free throws with 6:34 left in the first quarter.
Jennings followed with a layup, Ersan Ilyasova made a short jumper and Ellis dunked on a fast break for a 16-10 lead. It was 25-18 after one quarter before the Bucks held the Celtics to 12 points in the second quarter.
Boston improved its shooting in the third quarter, hitting 56.3 percent, but committed seven turnovers that led to 10 points.
"I don't like our urgency yet," Celtics coach Doc Rivers said. "When you watch us play, I don't like how we're approaching the games. And until we (improve) that, we're going to struggle."
Notes: The Celtics allowed the Bucks to hit 44.4 percent of their 3-point shots, one game after the Heat made 50 percent. Last season, Boston was the best in the NBA defending the shot at 30.8 percent. ... Milwaukee won its first season opener since Nov. 1, 2006, when it beat Detroit 105-97. ... Led by Ilyasova's 11 rebounds, the Bucks held a 51-41 advantage on the boards.