Davis scored 27 points and had a chance to win the game with the Heat down by one point, but his 17-foot jumper hit the rim twice and bounced out.
"It was a good look, it was what we wanted, it just didn't go down," Davis said. "It's tough, that's the kind of year we've been having."
The Heat went ahead 98-97 lead on Davis' free throw with five seconds left. Mobley then drew a foul while driving to the basket from Mark Blount with 2.6 seconds to go and hit both free throws to give the Clippers the lead for good.
"I tried to go into Blount and he tripped me," Mobley said. "I tried to scoop it up and the ref called a foul."
"We just pulled it out," Mobley said. "They made some shots in the second half and got themselves back into it. We got lackadaisical."
Mobley scored 18 points in the second half.
"Mobley gave us a big lift," Clippers coach Mike Dunleavy said. "In the second half he brought us back."
The Heat announced Monday that Wade will miss the remaining 21 games of the season due to pain in his left knee. Wade will undergo shock wave therapy on his knee in hopes of being healthy in time for the Olympics.
Daequan Cook had a career-high 23 points for Miami.
The Heat, who started the game with just eight players, the NBA minimum, mounted a furious comeback that fell short for their league-worst 51st loss.
Jason Williams tied the game at 94 with a 3-point shot with 1:13 left. The Clippers reclaimed the lead on two foul shots by Maggette with 53 seconds to go.
The Clippers broke a two-game losing streak.
"It was a collective effort," Maggette said. "They came at us with all they had. We're just glad we were able to withstand their big run."
The Heat, who trailed by 16 with 2:02 left in the second, took their first lead at 6:59 of the third when a Blount jumper put them ahead 64-63. Miami then went on a 23-4 run. The Heat led by 10 points with less than two minutes left in the third.
"We had a nice lead, then they got right back into it," Miami coach Pat Riley said. "Before we knew it, they were tied again and it was a game."
The Clippers' Chris Kaman sat out with a sore lower back. ... Elton Brand's return from a ruptured Achilles tendon this season is still in doubt. "We literally play every other day for the rest of the year," Dunleavy said. "It's hard to get the kind of practice time that he needs."
The San Antonio Spurs were in rare form in their demolition of the Oklahoma City Thunder on Saturday, but they refuse to rest on their Game 1 showing.
A disappointing 32-point loss for Oklahoma City in Game 1 of its series with San Antonio leaves the Thunder searching for answers.
When asked how he felt after Game 1 against the Spurs, Kevin Durant simply responds "I'm not telling you." When prodded a little more, he adds that they just need to move on to the next matchup instead of focusing on this one.