The Bolts started out strong at Dignity Health Sports Park, holding Green Bay to less than 10 yards in the first quarter, a feat that hadn't been accomplished for L.A. since 2012. Joey Bosa also contributed to the early lead, making his eight sack of the season in the same quarter.
Kicker Michael Badley made his first appearance of the season and made up for lost time after going 4-for-4 with field goals, giving the Bolts a nine-point lead by halftime.
Star running back Melvin also stepped into the spotlight by scoring two touchdowns during the game, including one in the fourth quarter.
Their lead was threatened late in the game after a touchdown and successful two-point conversion by the Packers.
Saturday's game marked the debut for the Bolts new offensive coordinator Shane Steichen.
Steichen replaced Ken Whisenhunt, who was fired Monday, one day after the Chargers failed to score more than 20 points for the sixth time in seven games.
City News Service contributed to this report.