The game reached the end of regulation time locked at 109-109 but the Heat pulled away in the extra period, Dwyane Wade scoring eight points in a run of 13 without replay to finish with 35 for the night.
LeBron James added a triple-double of 31 points, 11 assists and 10 rebounds as the Heat remained 4.5 games clear of the Atlanta Hawks, who beat the Charlotte Bobcats 104-92 as Josh Smith led the way with 30 points and 13 rebounds.
The Brooklyn Nets moved within half a game of the New York Knicks at the Atlantic Division summit with a 91-83 win over the Minnesota Timberwolves.
Brook Lopez top-scored with 22 points as the Nets backed up Monday night's victory over the Knicks to close the gap.
The South-West Division's leading pair, the San Antonio Spurs and the Memphis Grizzlies, both won to pull clear of the Houston Rockets, who were beaten by the Denver Nuggets.
The Spurs beat the New Orleans Hornets 106-102, with Tiago Splitter scoring 25 points and Tony Parker 24. Meanwhile, reports in America suggest this will be the Hornets' last season under that name before they become the New Orleans Pelicans from next season.
Memphis were resounding 106-93 winners over the struggling Los Angeles Lakers despite 29 points from Kobe Bryant, while James Harden's 23-point haul was in vain as Houston went down 105-95 at the Toyota Centre.
Ty Lawson scored 21 for the Nuggets as they closed on North-West Division leaders the Oklahoma City Thunder, who lost 104-99 to the Golden State Warriors. Stephen Curry top-scored with 31 points while David Lee had a double-double of 22 points and 12 rebounds.
Elsewhere in the North-West Division there were wins for the Utah Jazz, 92-88 against the Washington Wizards, and the Portland Trail Blazers, who downed Central Division leaders the Indiana Pacers 100-80.
The Chicago Bulls closed on Indiana with an 85-82 success against the Detroit Pistons, Jimmy Butler top-scoring with 18 points while Nate Robinson at one point scored nine successive points.
In the night's other game, Luis Scola's 21 points led the Phoenix Suns to a 106-96 win over the Sacramento Kings.