Miami embarked on a five-game road trip and found things difficult against a team trying to fight its way out of the Atlantic Division cellar.
The 76ers battled back from a 12-point halftime deficit and tied things up with 1:20 to go when Jrue Holiday scored on a dunk.
James then put Miami in front for good with a free throw and Wade scored a crucial basket on a tip-in of a James miss with 29 seconds remaining.
Two foul shots by Wade boosted the Miami lead to five points with 22 seconds to play and the Heat went on to extend the NBA's longest winning streak this year.
James scored 27 points to go with seven rebounds and eight assists while Wade contributed 21 points. Miami made 23 free throws to just seven for Philadelphia.
Miami's trip will continue with stops in Milwaukee, Toronto, Boston and Cleveland.
The 76ers were led by 24 points from Thaddeus Young and 21 from Holiday.
Miami tied idle San Antonio for the most victories in the league with 49.
Welker to join Denver Broncos
ENGLEWOOD, Colo., March 13 (UPI) -- Longtime New England Patriots receiver Wes Welker has agreed to a contract with the Denver Broncos, the Broncos said Wednesday.
"Agreed to terms on a 2-yr deal with Wes Welker," Broncos Executive Vice President John Elway posted on his Twitter account. "Excited to have Wes join the Broncos. His production & toughness will be a great asset!"
Welker is a five-time Pro Bowl selection, earning the honor each of the last five seasons. He was named All-Pro in 2009 and 2011. He led the NFL in receptions three times, most recently in 2011.
Welker caught 118 passes for 1,384 yards and six touchdowns last season.
Welker, who will be 32 before next season, caught 672 passes for 7,459 yards and 37 touchdowns while with the Patriots.
He was with the Miami Dolphins for three seasons before that, although his first NFL game was with San Diego in 2004, before he was released and picked up by the Dolphins. He was traded to New England prior to the 2007 season.
Bryant struggles, Hawks cool off Lakers
ATLANTA, March 13 (UPI) -- Kyle Korver's three free throws in the final 16 seconds Wednesday allowed Atlanta to hold on for a 96-92 decision over the Los Angeles Lakers.
The Hawks cooled off the Lakers, who had won four in a row but could not come through with the big shot they needed down the stretch.
Los Angeles superstar Kobe Bryant hit a 3-pointer with 18 seconds left to bring the Lakers within one, but he missed three other shots during the closing 90 seconds.
After Bryant gave the Lakers a chance with his 3-pointer, Korver hit 1-of-2 from the foul line. Bryant then missed a fadeaway jumper in a bid to tie it with 4 seconds left and Korver grabbed the rebound.
Korver's two free throws with 2.6 seconds remaining clinched the victory, ending the Hawks' three-game losing streak.
Devin Harris led Atlanta with 17 points and Korver had 15. Bryant had 33 points, but went 11-of-33 from the field while the Lakers were shooting 39 percent as a team.
Los Angeles is in the midst of a stretch in which it will play 8-of-10 on the road.
Bucknell wins second straight NCAA trip
LEWISBURG, Pa., March 13 (UPI) -- Mike Muscala ignited a decisive late run Wednesday that lifted Bucknell into the NCAA Tournament with a 64-56 win over Lafayette in the Patriot League final.
Bucknell earned a trip to college basketball's big show for the second straight year and for the sixth time overall. The Bison will be seeking their first NCAA victory since an upset decision over Arkansas seven years ago.
Lafayette closed within 43-40 with 6:34 to go on a jumper by Dan Trist, but then went scoreless for the next 3:30.
Bucknell produced 12 straight points, touched off by a hook shot from Muscala.
Muscala finished with 20 points and 11 rebounds, helping the Bison improve to 28-5. Bucknell won the regular-season championship in the Patriot League and hosted the title game against the second-seeded Leopards.
Joe Willman added 14 points for Bucknell, which converted 18 free throws to seven for Lafayette.
Joey Ptasinski had 15 points off the bench to lead the Leopards (19-15).
Celebrity Families of 2014 [PHOTOS]