After spotting the Jaguars a 14-10 lead late in the second period, Rivers drove the Chargers 68 yards on eight plays, capped by a 22-yard scoring strike to Vincent Brown, to put San Diego (5-7) ahead for good with 1:26 left in the half.
Eric Weddle then picked off Blaine Gabbert at the Jacksonville 39-yard line with 54 seconds remaining, and two plays later Rivers (22-of-28, 294 yards, no interceptions) connected with Vincent Jackson on a 35-yard TD toss for a 24-14 Chargers lead at the break.
Matthews added a 31-yard scoring run and Malcolm Floyd hauled down four passes for 108 yards and a touchdown in the victory.
Gabbert completed 19-of-33 pass attempts for 195 yards, a pair of TDs and an interception for the Jaguars (3-9), who lost their third straight.
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