Mitchell also had eight assists while Bojan Bogdanovic finished with 20 points and six rebounds and Joe Ingles came off the bench to score a season high 16 points for the Jazz, who ended a two game losing skid.
"I was just trying to find ways to get my teammates involved and make it easier on myself," Mitchell said. "We had more urgency. We lost two games because of offensive rebounds so we practised hard and it showed tonight."
Mike Conley scored 15 points while Rudy Gobert delivered 14 points and 16 rebounds in the win.
Simmons had just two points in 10 minutes before leaving with 5:20 left in the second quarter with right shoulder injury. Simmons reportedly has a sprained AC joint and will be examined by team doctors on Thursday.
Embiid finished with 27 points and 16 rebounds but was just five of 16 from the field as Philadelphia lost its second straight game. Josh Richardson scored 24 points, Tobias Harris added 16 and Raul Neto had 11 for the 76ers.
James Harden finished with 36 points and 13 assists and shot six of 16 from beyond the arc for the host Rockets in front of a crowd of 18,000 at the Toyota Center arena.
"I pick and choose when I have to be aggressive," Harden said. "It is a process and we are building something great."
Harden has now shot 13 of 32 from three point range in his last two games after shooting just 17 of 79 in his first six games of the new season.
The contest was expected to be a high-scoring affair as the Rockets and Warriors are 29th and 28th in the NBA in points allowed.
The Rockets give up an average of 123 points per game and the Warriors 120. Neither team has been able to hold their opponent to under triple digits so far this year.
The lineup the Warriors used Wednesday was a shadow of the team that reached the NBA finals last season where they lost to the Toronto Raptors.
"Hopefully those guys will get back in the court soon. That is the league, injuries happen," Harden said. "We had that problem a couple years ago. So it's nothing new."
Against the Rockets, Golden State was also without D'Angelo Russell (sprained right ankle) and Draymond Green (injured finger) for a third straight game.
Russell Westbrook had 18 points, eight rebounds and six assists before leaving the contest with an unspecified injury.
- Raptors home cooking -
Lowry has scored 20 or more six times in Toronto's first seven games. Marc Gasol each scored a season high 12 for Toronto.