A 36-yard field goal by Nick Novak and Rivers' TD pass to Woodhead — which was set up by Marcus Gilchrist's recovery of Andre Brown's fumble — helped the Chargers take a 24-0 halftime lead.
The Chargers blew a 24-0 halftime lead to Peyton Manning and the Broncos last year, but weren't about to do to same to Manning's little brother and the Giants.
Rivers was sacked by Justin Tuck and fumbled on the first possession of the second half, with Cullen Jenkins recovering at the 18 to set up Peyton Hillis' 1-yard scoring run.
Rivers appeared to injure his neck when he dove for the loose ball but stayed in the game.
Mathews scored on a 1-yard run to cap an 11-play, 80-yard drive that was all on the ground except for a pass from Rivers to Vincent Brown that drew a 36-yard pass interference call against linebacker Spencer Paysinger.
Manning threw a 5-yard touchdown pass to Brandon Myers and Novak added field goals of 27 and 43 yards, all in the fourth quarter.
NOTES: A moment of silence was observed for Nelson Mandela before the national anthem. ... Chargers OLB Melvin Ingram made his season debut after tearing up his left knee in May. He had one tackle.