Erik Spoelstra's bunch looked lethargic for most of the night, playing with tired legs on the second night of a back-to-back, but their effort late was enough to get the job done.
The Sixers wound end up making a strong push in the fourth quarter, but the Heat's ability to convert in clutch situations in the game's final stanza was enough to slip by a Philadelphia team that fell to 24-40 with the loss.
Next up for the Heat is a meeting with the eighth-seeded Milwaukee Bucks on Friday night.
Mario Chalmers, PG: D
It was an off night for Mario Chalmers, who couldn't find his stroke from distance early. Typically when Chalmers is able to work himself into a groove within the game's first six minutes, the Heat are going to have themselves a good night.
Against the Philadelphia 76ers, Chalmers was faced with a difficult matchup against All-Star point guard Jrue Holiday, who finished with a complete stat line of 21 points, seven rebounds and seven assists.
Although Chalmers posted a plus/minus of plus-13, it was largely a product of being paired up with LeBron James and Dwyane Wade throughout the evening.
Finishing with just seven points on 3-of-9 shooting (0-of-5 from three), Chalmers simply didn't have it working against the Sixers.
Dwyane Wade, SG: B+
It wasn't his most efficient game of the Heat's win streak, but Dwyane Wade was effective nonetheless.
Wade's scoring numbers were down just a touch, as he scored 21 points on 7-of-14 shooting, but he was active in other ways, securing eight rebounds while dishing out three assists.
With favorable matchups against Damien Wilkins and Royal Ivey, Wade was able to pick his spots and go to work when he pleased. His all-around game was crucial to Miami's win.
LeBron James, SF: A
A slow start had the Heat's 19-game win streak looking like it was at risk of being snapped, but LeBron James' tenacity and aggression ramped up as the game went on, propelling the Heat to their 20th straight victory.
James was just about the only Heat player who came out firing early and often on Wednesday night, recording nine first-quarter points on 4-of-6 shooting.
Functioning as the team's primary ball-handler, James turned the ball over three times in the game's first period, but would do so just once over the final three quarters.
A flurry of highlight-reel slams keyed an 11-0 Miami run toward the end of the second half, as LeBron showed that he would not be outdone by a competitive Evan Turner.
LeBron finished with 27 points on 8-of-19 shooting (including a clutch 10-of-12 shooting from the free-throw line), seven rebounds and eight assists.
Udonis Haslem, PF: B
Udonis Haslem's impact on Wednesday night's victory was fairly negligible, but he chipped in with hustle and effort on the defensive end.
Totaling four rebounds in 18 minutes of play, Haslem flashed his trademark toughness by constantly throwing his body in front of an athletically superior Thaddeus Young.
Playing in a platoon with Chris Andersen, Haslem's job has been to pack a defensive punch, take charges and set hard screens on offense, and he did just that.
Chris Bosh, C: C
With LeBron James and Dwyane Wade running the show on offense, Chris Bosh was held to few opportunities, the bulk of which he failed to take advantage of.
Bosh's energy level picked up considerably in the second half, but his final output was far below what we've come to expect of the eight-time All-Star.
Converting on a measly 5-of-11 attempts from the field, Bosh didn't bring nearly enough on a night when the Heat were pushed to the limit by a feisty Philadelphia squad.
The fact that Bosh couldn't manage to exploit a matchup against Spencer Hawes tells you all you need to know about his performance tonight.
Bosh finished with 10 points and five rebounds.
Ray Allen, SG: B+
He didn't see a ton of action, but Erik Spoelstra chose to go with Ray Allen over Shane Battier in crunch time against the Philadelphia 76ers.
It turned out to be the right move.
Allen hit one of the two threes he canned on the night when the Heat found themselves down two late in the fourth quarter.
Finishing with 12 points on 3-of-5 shooting (2-of-4 from three), Allen was a key reason why the Heat escaped with a win.
Rest of Bench: B-
As was to be expected, Erik Spoelstra only utilized four men off of his bench on Wednesday night, employing a reserve grouping that consisted of Chris Andersen, Shane Battier, Norris Cole and Ray Allen.
Andersen was his usual, active self, setting strong picks while rolling to the basket en route to easy, uncontested dunks. The Birdman even converted on a couple jumpers and came up with a massive block of Spencer Hawes down the stretch.
Battier struggled more than usual to find his stroke, knocking down 2-of-6 shots from beyond the arc en route to six points.
As always, Battier was overshadowed, and he made the Sixers pay for doubling up on LeBron James by knocking down a couple of open looks from the corner.
Cole was a non-factor in his 13 minutes, posting a big doughnut in the scoring column.