The Heat, though, are looking for an improved defensive effort all around.
Allen and Bosh are seeking to build on strong performances in order to help Miami to its fifth straight victory over the Phoenix Suns on Monday night.
Allen came up big in just his third game for the Heat (2-1) on Saturday, converting a four-point play with 6.7 seconds left to help secure a 119-116 win over Denver. The 37-year-old guard finished with 23 points, hitting 6 of 10 from 3-point range.
The Heat know all about Allen's abilities beyond the arc since he made 47.5 percent in 32 games against them while with Boston, including 17 postseason contests.
"We've been on the other end, as the recipient of that type of pain, in the locker room when he puts the dagger to your heart with a 3 - and the and-one, just for the heck of it," coach Erik Spoelstra said. "Do we expect him to do that every single night? That's not necessarily what he has to do. It's what he's done his whole career, but he's found a way to fit in."
With more efforts like Saturday's, Bosh will continue to fit in just fine on Miami's star-studded roster. He scored 40 points - his most since joining the Heat - while making 15 of 22 shots against the Nuggets after totaling 31 over the first two games of the season.
Bosh could be in for another productive performance since he's averaging 27.9 points over his last eight meetings with Phoenix (1-2), scoring a game-high 29 in a 99-95 home victory March 20.
The Heat may be more eager to see some improvement defensively. They're allowing opponents to average 109.0 points after holding them to 92.5 last year - fourth-best in the NBA.
"We haven't been playing our best basketball," Bosh said. "We know we've gotten off to a slow start defensively. We have to pick that up."
Facing Phoenix could be just what Miami needs to re-establish its defensive dominance. The Heat have won four in a row and seven of eight against the Suns, who enter this meeting averaging 90.3 points on 42.2 percent shooting - 21.6 from beyond the arc.
They're also coming off their worst defensive performance so far, allowing Orlando to shoot 48.9 percent in Sunday's 115-94 loss. Phoenix, still adjusting after Steve Nash's departure, shot 35.6 percent in the second half.
"I think we're struggling somewhat to have consistency offensively," coach Alvin Gentry said. "But we're a work in progress and we continue to work and try to get better and we'll see what happens."
Luis Scola had 24 points against the Magic, four shy of his total from the previous two games. The Argentinian forward has averaged 20.7 points in his last three matchups with Miami.
Phoenix's Michael Beasley scored 22 points Sunday, but has just 28 over three meetings with the team that drafted him second overall in 2008.
LeBron James will be looking to take advantage of the struggling Suns after coming one rebound shy of a triple-double Saturday with 20 points, 11 assists and nine boards. James has averaged 29.0 points in 17 career meetings with Phoenix.