Garnett missed the last two contests while dealing with the flu and a strained abductor, but coach Doc Rivers said Garnett was close to playing against Miami on Monday. The Celtics (36-30) are 2-1 without Garnett this season.
Boston led by 17 in the first half against the league-best Heat, but LeBron James' go-ahead basket with 10.5 seconds left gave Miami a 105-103 victory that extended its winning streak to 23.
Jeff Green carried the Celtics offensively with a career-high 43 points. In the three games without Garnett, Green has averaged 28.0 points while going 30 for 44 from the field and 8 for 13 from 3-point range.
Paul Pierce added 17 points, eight rebounds and eight assists but missed a 3-pointer in the final seconds that could have given Boston the win.
"No moral victories, even though it was a close game," Pierce said.
The Celtics had won seven of nine before falling to the Heat, but the two losses came on the road by an average of 19.0 points. Boston is opening a three-game trip and plays six of eight away from home.
A date with the league-worst Hornets could give the Celtics a good chance to get the stretch started with a win. New Orleans (22-46) lost its fourth straight and 12th in 15 games Monday, 93-72 to Golden State in the opener of a seven-game homestand.
Ryan Anderson had 21 points and Anthony Davis added 16, but the Hornets shot 33.7 percent from the field and 3 for 17 from 3-point range.
"We took a lot of bad shots," coach Monty Williams said. "It's a challenge to try to manufacture your offense with guys who are trying their best to make shots when we don't have a guy to get it done, get the ball and go to the basket."
Despite its recent struggles, New Orleans has won four of five meetings with the Celtics and can sweep the season series following a 90-78 victory Jan. 16.
The Hornets rolled to the surprisingly victory in part by dominating the boards, holding a 55-40 advantage. That could again be an area of concern this time for the Celtics, who rank near the bottom of the NBA in rebounding differential at minus-3.8.
Davis has averaged 17.3 points and 10.3 rebounds in his last six games overall.
Garnett led Boston with a team-high 15 points in the first meeting, but he's scored 9.0 per game and shot 37.5 percent in his last three at New Orleans.