Bosh said he knew he had to up his scoring with Wade out.
"I know that my role has changed a bit and I have to be a lot more aggressive so it's just a matter of making shots when I'm open," he said.
After his starters got off to another sluggish start, Phoenix coach Alvin Gentry said there would be a change in the lineup, although he didn't say what that would be.
"We have to make some adjustment," he said. "We can't keep playing like this. We have to do something where we can make an adjustment and we'll see what can happen from here."
Dragic said the team will follow Gentry's lead.
"I mean, he's the coach so whatever he says, he is going to run this team," Dragic said. "You know, something is not clicking for us and we have to find some solution. If that is he has to change some players in the starting lineup then we have to do that."
James had a dunk on a lob pass from Mike Miller and sank a 3-pointer in a 19-4 outburst that broke a 56-56 tie and put the Heat up 75-60 after Norris Cole's steal and layup with 2:52 left in the third quarter. But James went to the bench and the Suns' reserves brought Phoenix back with an 11-0 run to end the quarter, reducing Miami's lead to four entering the fourth.
Morris scored the first six points of the run. Miami committed two turnovers in the final minute of the quarter, leading to Brown and Telfair each sinking a pair of free throws.
Bosh had 16 points on 6-of-7 shooting in the first half. Beasley had 12 points and five first-half rebounds.
NOTES: Dragic had eight points, four assists, three steals and no turnovers in the first quarter. ... The Heat have one more six-game road trip, Jan. 1-17, a journey that concludes with a game against the Lakers in Los Angeles. ... This was Miami's first trip to Phoenix in two seasons. The teams played only once, in Miami, in the lockout-shortened 2011-12 season. ... Miami had 19 turnovers, compared to 17 for Phoenix.