The 76ers rallied from what had been a 13-point deficit in the third quarter to win for the third time in four games.
Covington, who finished with 16 points, and Saric combined for nine points in the NBA contest's final 5:27 as the 76ers rallied from what had been a 13-point deficit in the third quarter to win for the third time in four games.
Al Horford scored a season-high 27 points and contributed eight rebounds and six assists to lead the Celtics, who fell to 44-26, two games behind Eastern Conference leader Cleveland.
The Celtics, whose three-game win streak ended, were without All-Star guard Isaiah Thomas, who rested a sore right knee. He is expected to return Monday against Washington, third in the East at 42-27.
With the score knotted at 91-91, Covington sank his crucial 3-pointer and 76ers guard T.J McConnell sank a jumper that triggered a 9-2 Philadelphia flurry to seal the win.
The Memphis Grizzlies' title hopes took a blow Sunday as they announced forward Chandler Parsons will undergo left knee surgery on Monday and is expected to miss the rest of the season.
Parsons, 28, will undergo a procedure to repair a partial tear of the medial meniscus.
He had signed a four-year contract worth $94 million with the Grizzlies in the offseason but has averaged only 6.2 points in 34 games this season, nagged all season by knee injuries.
Parsons has undergone two surgeries on his right knee in two years.