Memphis outscored Miami 9-2 in the final 2 minutes for its second win in the last three.
"That's a big difference for us, when it comes down to the end of the game to make plays and make sure we get the win at home," Gasol said.
The teams were tied at 92 with 2 minutes left. Gasol scored inside with 1:57 remaining to give the Grizzlies the lead, which they maintained when Wade, a 75 percent free-throw shooter, missed a pair from the line with 1:04 left.
From there, Memphis hit its free throws to hold on. The last time Miami lost seven straight was the opening of the 2003-04 season.
"When I missed those two free throws, it kind of took the air out of us as a team for the next couple of possessions," Wade said. "It was like we did everything wrong that we could do."
It was an extension of the Heat's fourth-quarter woes. Miami was 23-15 in the final period of a 94-89 loss at Dallas on Friday night and is 2-20 when trailing entering the fourth. Memphis held a 70-66 lead after three on Sunday.
"We played extremely well in the fourth quarter with the exception of the last several shots in the game, and a couple of free throws and maybe a couple of offensive rebounds," Heat coach Pat Riley said. "...We must have the wrong players in the game. It's the wrong mix or something in the fourth quarter. I think I have the right mix, but I must have the wrong mix."
Haslem added: "I don't know if it's a mental thing, if it's in our heads, or we don't believe. But, for whatever reason, we just can't get it done."
Wade, Shaquille O'Neal and point guard Jason Williams, who have been limited recently by a variety of injuries, dressed but did not start for the Heat. Wade and Williams entered the game in the first quarter, but O'Neal's left hip bursitis kept him on the Miami bench all day.
Memphis led by as many as nine in the second half, but neither team could gain a double-digit lead in the game.
The rest of the stats were just as close, as Memphis controlled the boards 44-37, but 12 of the Heat's were on the offensive glass. Memphis outscored Miami in the paint 42-36, while the Heat shot 46 percent from the field to 47 percent for Memphis.
Miami used a second-quarter rally to take a 46-43 lead into the break. Davis had 11 points to lead the Heat, hitting four of his first five shots.
Wade, who sat out Friday's game against Dallas, missed seven of his nine first-half shots. His five points before the break were the only scoring off the Miami bench. Meanwhile, the Grizzlies' reserves managed only two points, and missed eight of nine shots.
Wade was the only Miami play to score off the bench in the game, while Memphis managed only seven points from its reserves.
"I'm a rhythm player," Wade said. "I knew early on I was going to miss some shots to get my rhythm back, and I wanted to do it early in the game so I could have it later. It was just about getting my overall rhythm back."
Miami weathered missing its first five shots in the second half. Davis had 10 points in the third, but Memphis managed to carry a 70-66 lead into the final period.
Memphis has lost six of seven games this season decided by three points or less.
"Any time you want to win games, you've got to make stops down the stretch," Miller said. "They had capable scorers. Dwyane's a great basketball player. Ricky Davis had it going. We had to make some stops down the stretch, and we did that."
Miami reserve C Earl Barron played collegiately at Memphis, and reserve F Alexander Johnson was with Memphis for his rookie season last year. ... Veteran Grizzlies G Damon Stoudamire was on the inactive list for the third straight game as Memphis is going with rookie Conley and second-year player Kyle Lowry at the point. ... Daequan Cook, the rookie from Ohio State, started his second game of the season and finished with nine points. ... Heat C Mark Blount (12 points) started his third straight game. He has reached double figures in all three starts. ... Williams had missed the previous five games with an inflamed left knee and was held scoreless in 15 minutes. "JWill hasn't played since before Christmas," Riley said. "He hasn't even shot the ball. We need some support. He needed to come in and try. He's off his game."