Simmons poured in 27 points to go with 15 rebounds and 13 assists to record his 12th triple double of the season - fourth before the end of the third quarter - but the Sixers needed every bit of it as James poured in 44 points to go with 11 rebounds and 11 assists.
He scored 13 points over the final six minutes, and either scored or assisted on eight of Cleveland's last nine field goals.
With the win over the Wizards (42-37), the Cavaliers (49-30) took a half-game lead over the Philadelphia 76ers for the No. 3 seed in the Eastern Conference standings with just three games to play in the regular season, including Friday night's contest against the 76ers in Philadelphia.
LeBron James split a pair of free throws to make it a one-point game with 52.9 seconds left, which was followed by a stop from the Cavaliers' defense.
First, he missed a 23-foot bomb while holding a one-point lead.
Jokic finished with 16 points and 14 rebounds, while reserve Devin Harris added 20 for the Nuggets.
Dominating at the offensive end, the 33-year-old James hit a pair of free throws to cut Washington's lead to 110-106 with 2:40 to go, then fed Green for a dunk that made it a two-point game at the 2:07 mark.
The Toronto Raptors clinched the top seed in the Eastern Conference with a 92-73 win against the Indiana Pacers, while the Minnesota Timberwolves toppled the Los Angeles Lakers 113-96 and the New Orleans Pelicans defeated the Phoenix Suns 122-103.
Washington is going to the playoffs and Philly is on the path to becoming the next great team for years to come.
Markieff Morris had another understated yet productive all-around game Wednesday with 15 points, five rebounds and four assists. But he had a costly turnover in the closing seconds and the Wizards couldn't put away the Cavs down the stretch.
Much to the joy of National Basketball Association fans, the two teams will go mano-a-mano tonight at the Wells Fargo Center in a high-stakes showdown that will have major implications on their eventual playoff success, and the legacies of every player involved.
"We just played our game, didn't let the hype bother us and we stuck together". Now, they have Kevin Love back and are playing some of their best ball of the season. Things only got worse in the third, as Cleveland was outscored 64-43 over the middle quarters yet somehow found a way to win. During a recent segment of ESPN's First Take, Will Cain said he thinks McCollum is on to something when he suggested Philadelphia as James' landing spot this summer.