San Antonio, though, has a run of its own going, too.
Miami seeks to remain unbeaten at home while the Spurs look to complete a perfect six-game road trip as the streaking teams meet Thursday night.
The Heat (10-3) have won their first six games at American Airlines Arena and earned their fourth consecutive victory overall with a 110-108 come-from-behind win over Cleveland on Saturday.
Chris Bosh finished with 23 points and Allen had 17 off the bench for the Heat, who trailed by seven with 1:58 remaining.
''It speaks to the competitive will that the guys have at the end of close games,'' coach Erik Spoelstra said. ''We have a lot of gamers in that locker room. They rise to the occasion. They want situations like that. That can be dangerous, as well.''
That's especially true at home, where the Heat have won 28 of their last 30 regular-season games and 10 straight including the playoffs.
They've also dominated the Spurs in their last two games at Miami, getting 30 points from Bosh in both victories - a 110-80 win March 14, 2011 and a 120-98 rout Jan. 17, when James had 33 points and 10 assists.
A similar result doesn't seem as likely given how well the Spurs have been playing during their trip.
''It's early. We'll lose our share, but right now we're playing pretty well, I guess,'' coach Gregg Popovich said. ''It's our second road trip this month. I think they do deserve credit for keeping their focus all that time.''
Tim Duncan added 15 points for the Spurs, who have won eight straight and 19 of their last 21 regular-season road games. A win would give San Antonio just its third unbeaten road trip with a minimum of five games in franchise history, with the others coming on five-game swings in 1984 and 1990.
''We're just playing basketball the way we've been playing it,'' Duncan said. ''Whoever is put in front of us, that's how we're playing. We've been playing well for a couple of games here and we hope to continue it.''
While San Antonio remains humble, Miami knows how dangerous the Spurs can be.
"Year in and year out, the Spurs are going to come into a season and not be one of the talked about teams in the NBA and they're going to have the best record in the league," said Dwyane Wade, who sat out the last meeting with a sprained right ankle. "It should be no surprise. You should come to expect it."
Spoelstra expressed similar thoughts.
"They've done a terrific job on the road even dating back to last season," he said. "They are a well-oiled machine."
San Antonio is allowing only 95.1 points per game, but Miami is the league's second highest-scoring team, averaging 104.8.
James, who is averaging 30.6 points in his last seven games versus the Spurs, ranks fourth in the NBA in scoring at 25.2 per contest.