Hayward hardly looked rusty, hitting 5 of 9 shots, including a pair of 3-pointers, to finish with 17 points in 25 minutes off the bench.
It didn't take long for his right shoulder to get a test.
He checked into the game with 4:35 remaining in the first quarter to loud applause. Two minutes later, he drove the lane and took a shot to the same shoulder from Andris Biedrins.
"It was good as far as realizing it would be fine if I took a hit," said Hayward, who has been Utah's third-leading scorer this season at 13.5 points a game. "It stung a little bit. But I stepped up and knocked down two free throws and moved on from there."
Jefferson said the Jazz now just need to get starting point Mo Williams back after he had thumb surgery in early January.
"Then I just think we keep rolling," Jefferson said.
The question is whether Jefferson and Millsap will be around to see the playoff run play out.
Both are unrestricted free agents after this season and have been the subject of trade rumors heading into Thursday's deadline.
"My name has been in trade rumors ever since my second year in Boston when they were trying to trade me for Allen Iverson," Jefferson said. "That was the rumor. Nothing happened then. Nothing ever happens. This year is going to be no different for me as far as focus. I will continue to stay focused and do my job."
Millsap made 4 of 4 from the line and also grabbed nine rebounds.
If Tuesday was his last game in a Jazz uniform, he wasn't distracted.
"Our team is good that we have now," he said. "These are rumors. That's what rumors are. Who knows who started them? Our job is to get out there and win games no matter who's here."
NOTES: Utah assistant Sidney Lowe was on the Jazz bench, coaching his first game since being arrested over the weekend in North Carolina for failing to file his state income tax returns for 2009, 2010, 2011. The team is referring all legal questions to Lowe's attorney, but coach Tyrone Corbin said," We support him wholeheartedly. He understands and has taken responsibility for where he is in it. We'll support him and move on." ... Corbin wouldn't talk specifics about Thursday's trade deadline, but said, "I love everybody on this team. Love what these guys bring, love how they stayed focused and try to get better. ... These are Utah Jazz kind of guys."