CLEVELAND, Jan. 21 (Ticker) -- Brian Grant was not going to return unless the Miami Heat needed him. They did, and he came through with the biggest shots of the game.

After receiving stitches midway through the fourth quarter, Grant returned and nailed two clutch jumpers in overtime to lead the Miami Heat to their season-high fifth straight win, 95-93 over the Cleveland Cavaliers, who have lost 10 in a row.

Grant went to the locker room after getting elbowed in the face by teammate Alonzo Mourning while going for a rebound with 7:08 remaining in the fourth quarter. He was only going to return if Miami blew its comfortable lead, which is exactly what happened.

NBA.comTV highlights from Heat-Cavs: 56k | 300k Alonzo Mourning meets great resistance from the Cavs at the rim. David Liam Kyle NBAE/Getty Images

The Heat had an 85-77 cushion with 94 seconds left, but the Cavaliers finished regulation on a 10-2 run. Zydrunas Ilgauskas scored six points during the spurt, including a pair of free throws with nine seconds left to tie it for the first time since the opening tip.

Ilgauskas opened overtime with a layup to give Cleveland its first lead. The Cavs took a 91-89 edge on a pair of foul shots by Andre Miller with three minutes remaining, but Eddie Jones, who scored 27 points, tied it on a floater 42 seconds later.

Grant gave Miami the lead for good, 93-91, on a 19-foot jumper with 1:22 to go, his first basket since the second quarter and Miami's second in a span of five minutes.

"The Cavs were staying home on Eddie and they were denying us," Miami coach Pat Riley said. "We were just running a simple high pick-and-roll and were fortunate that Ilgauakas had to play (Rod) Strickland a little bit and recover."

"(Grant) went out and made some big plays and I'm the one who took him out of the game," Mourning said. "I told him when he came to the bench in a timeout, `Take this thing over, do what you have to do. Don't let them take it from us.'"

Grant sank another jumper from nearly the same spot with 46 seconds left.

"I was just thinking that (Ilgauskas) was going to rotate to me slowly," said Grant, who finished with 10 points and eight rebounds. "I know I can hit the shot, so I didn't hesitate or second-guess myself. I just let it go."

Former Heat Ricky Davis' jump shot with 31 seconds left halved the deficit and Cleveland had the game's final possession. But Jumaine Jones missed a 3-pointer at the buzzer.

"We got exactly what we wanted, we got a look," Cavs coach John Lucas said. "I told Jumaine in the huddle, `If Andre throws it to you, win us the game and let's go home.'"

Miami secured its first five-game winning streak since April 4-11 and avoided a sweep in the season series with Cleveland for the first time since the 1989-90 season.

Mourning scored 15 points before fouling out late in the fourth quarter. His absence was a key reason Cleveland was able to rally.

Jones hit a fadeaway jumper with 1:34 remaining before Wesley Person, who scored 19 points, converted a three-point play to spark the comeback.

Jones missed a jumper and Ilgauskas sank a pair of free throws to bring the Cavs within 85-82 with 75 seconds left. After Mourning and Ilgauskas exchanged misses, Strickland threw a pass out of bounds with 26 seconds to play.

Miller missed second of two free throws three seconds later and Mourning grabbed the rebound. He was fouled but made just 1-of-2 at the line, giving the Heat an 86-83 edge.

Miller fired an airball from 3-point range, but Ilgauskas caught it and wound up with an easy layup. Strickland missed the back end of a pair of free throws and Mourning was called for a costly loose-ball foul.

Ilgauskas buried the resulting free throws to tie it and Miami missed two shots on its final possession, including a wide-open jumper by Jones as time expired.

"We let them back in it, making silly fouls and loose ball fouls and risks that you normally don't take," Riley said. "We got the win, that's all it was about. But I don't think we should have gone into overtime to do it."

Strickland had 13 points, seven assists and six rebounds and rookie Mike James scored a season-high 12 points for Miami, which shot 48 percent (38-of-80) and made 7-of-12 3-pointers.

Miller finished with 17 points and 12 assists for the Cavs, who have lost 10 straight games for the second consecutive season. They also dropped 10 in a row from January 27-February 17, 2001.

Jumaine Jones scored 14 points and Ilgauskas added 13 and nine rebounds as Cleveland shot just 41 percent (33-of-80) and lost despite outscoring Miami, 24-12, at the line.