The 6-1 Saints are battling for the top seed in the NFC.
Chase Edmonds was stopped at the line of scrimmage, and five plays later, Brees found Murray for a 15-yard catch and run that widened New Orleans' lead to 17-6.
"I know the thought would be, 'Why don't you just wait until after the bye week (to return)?,' " Brees said after this win.
The Jets doubted the severity of the injury and team physicians cleared Osemele, who has not played since Week 3.
It might seem trivial, but there are different gameplans for different quarterbacks and what the Saints do with Brees under center is going to be drastically different than what they do with Bridgewater under center.
The 26-year-old has thrown for 1,370 yards, nine touchdowns and two interceptions this season, with a completion rate of 67.7 percent.
New Orleans is 1-2 in the last three games in which it has given away a double-digit point spread at home. Murray will once again dominate the backfield touches for New Orleans, as is evident by him playing 83% of the team's offensive snaps last week.
They enter their bye week after this Sunday, meaning that if Brees didn't play against Arizona, he'd have seven weeks of rest before returning in Week 10 against Atlanta.
Teddy Bridgewater has been magnificent in Brees' absence, winning the hearts of Saints fans while winning every game he has started since stepping in for the future Hall of Famer. Arizona was held to 40 yards rushing and the Saints' defense held a fifth-straight opponent below 260 total net yards. "We continue to get better and better in all phases". "We'll see. Both those guys got a lot of work this week". The second-year wideout comes back at a flawless time as Arizona attempts to spoil New Orleans' five-game winning streak.
Kirk has missed the past three weeks with an ankle injury that he sustained in Week 4 against the Seattle Seahawks. Not practicing were WR Tre'Quan Smith (ankle), TE Jared Cook (ankle), RB Alvin Kamara (ankle/knee), CB Patrick Robinson (hamstring) and S J.T. Gray (ankle).