Stephen Gostkowski booted field goals of 41, 49 and 35 yards for the Pats (3-1).
Faulk's touchdown runs were each from the 2-yard line.
New England quarterback Matt Cassell completed 22-of-32 passes for 259 yards and a touchdown, with two interceptions. The scoring pass went to Moss on a 66-yard play.
J.T. O'Sullivan tossed three scoring passes but was picked off three times for San Francisco (2-3).
Isaac Bruce caught two touchdown passes and Frank Gore carried 12 times for 54 yards and caught four passes for 24 yards and a touchdown for San Francisco.
Notable deaths of 2014 [PHOTOS]