"I got eyes on the rim and just let it go," Harris told reporters after the 107-106 win on Wednesday in Philadelphia.
LeBron James scored a game-high 34 points for Los Angeles. The setback was the Lakers' first road loss of the season.
"We gave ourselves an opportunity to win at the end and it didn't go our way," James said.
The Lakers used a 13-0 run to take a 106-105 lead with 11.2 seconds remaining before Harris ended the Sixers' streak of more than three minutes without a score.
Simmons started the play with an inbound pass from the left sideline. Seth Curry caught the feed before he dribbled right and then went back to his left, which allowed Harris to switch off to a smaller defender.
Curry then passed off to Harris, who took a few dribbles to his left. Harris then drove to the rim before he elevated and made his final shot over Lakers guard Alex Caruso.
Lakers forward Anthony Davis missed the final attempt of the game to give the Sixers the win.
Embiid scored 13 points in the first quarter to lead the 76ers to a 34-24 edge. The Lakers then outscored the Sixers 27-21 in the second quarter, but still trailed 55-51 at halftime. The Sixers increased their lead to seven points after the outscored the Lakers 26-23 in the third frame.
The Lakers outscored the Sixers 32-26 down the stretch, but couldn't hang on to their late advantage.
"Like champions, it was hard to kill them," Sixers coach Doc Rivers said of the Lakers. "They kept coming back and kept believing and making shots.
"This says that we are a good team, but we still have a lot of work to do."