Spencer Hawes had 19 points and eight rebounds for the Sixers, who hadn't won away from Philadelphia since their road opener on Nov. 1.
Young and Michael Carter-Williams contributed big points down the stretch as the last-place Sixers held on for just their second win in 11 games overall.
Nick Young scored 26 points on 6-for-21 shooting in the Lakers' fifth consecutive loss. Los Angeles also has lost five of six at Staples Center, winning just once at home since Nov. 24.