Embiid, who had engaged in a war of words with Detroit center Andre Drummond earlier in the day, added 10 rebounds. He made just 7 of 21 shots from the floor, however.
Drummond, who fouled out with 2:35 left, finished with 14 points, 11 rebounds and six assists.
Sixers forward Dario Saric, who scored 17 points, keyed an 18-6 run late in the game with two 3-pointers -- the first of which put Philadelphia ahead to stay at 92-91 with 6:06 left.
That flurry wiped out an 89-86 deficit and gave the Sixers a 104-95 cushion with 1:25 remaining.
The Pistons later closed to 106-103 on a 3-pointer by Langston Galloway with eight seconds to play, but Sixers guard J.J. Redick nailed two free throws with six seconds remaining.
Redick contributed 18 points for Philadelphia (13-9), which won for the second time in three games.
Earlier in the day, Embiid told reporters that Drummond "can't shoot," and Drummond responded by telling reporters that you "can't really have a conversation with a man who can't play a back-to-back." That was a reference to the Sixers' policy of resting Embiid when the team plays on consecutive days.
The Sixers erased an early eight-point deficit by reeling off 15 straight points, six each by Covington and backup center Amir Johnson, and led 32-25 after a quarter.
They extended that to 63-47 at halftime, at which point Embiid had 15 points and Covington had 14.
Harris led the Pistons with 10 points.
Jackson rallied Detroit by scoring 12 points in the third quarter, including two 3-pointers. The Pistons also forced nine Philadelphia turnovers while outscoring the Sixers 33-17 in the quarter, forging an 80-80 tie entering the fourth quarter.
The Pistons took their first lead since the opening quarter at 84-82 on Drummond's dunk with 10:04 left in the game, and later went up 89-86.
Covington then dropped in three free throws after being fouled on a 3-point attempt with 7:04 remaining, triggering the Sixers' game-ending flurry.
NOTES: Detroit coach Stan Van Gundy dismissed the pregame byplay between Sixers C Joel Embiid and Pistons C Andre Drummond as "just noise," but Philadelphia coach Brett Brown said it was Embiid's way of getting himself motivated to face another top-notch center. "He loves it," Brown said. "Has he tweeted about it yet? He loves it, and it's part of his gamesmanship. ... He just loves a challenge. He winds it up. He doesn't hide from any of it." ... The Sixers were without PG T.J. McConnell (shoulder sprain) for the second straight game. "You miss a bite," Brown said. "There's a bite he gives us. There's a sting to everything, and there's a pace to everything." ... Philadelphia G/F Justin Anderson (shin splints) missed his eighth straight game. .... Pistons F Jon Leuer (ankle sprain) sat out his 14th straight.