It was the Giants' first rushing touchdown of the season by a running back.
In his last season at Clemson, Williams played in 15 games and caught 98 passes for 1,361 yards and 13 touchdowns.
Late in the first quarter, Darkwa took a hand-off to the right, broke a tackle and ran it in from 23 yards out. NY has not beaten the Chargers (1-5) since 1998.
Tre Boston intercepted the Giants quarterback, who lost four receivers to injury during the game, on fourth down in the final minute to seal Anthony Lynn's first professional victory.
This is the Giants' worst start since the 2013 season.
The Giants quarterback recorded all 80 yards through the air, completing 6-of-7 passes in the process. "If it wasn't for him, I'd be playing in a soccer stadium", per Newsday's Bob Glauber.
Rivers' tenure with the Chargers has been good, but the team advanced to one AFC title game, losing to the Patriots after the 2007 season.
Prior to Darkwa's score, the Giants got a safety when Chargers center Spencer Pulley snapped the ball before Rivers was ready.
The Giants (0-5) jumped out to a 9-0 first-quarter lead, which included their first points scored on offense in the first quarter since a 22-yard field goal by Robbie Gould in the 2016 regular-season finale against Washington.
Manning had given the Giants a 22-17 lead early in the fourth quarter with a 48-yard TD pass to a wide-open Beckham. All told, he accounted for 163 yards from scrimmage and two touchdowns in the team's first win of 2017.