Coming off a franchise-best 517 yards through the air last Monday in Miami, Brady finished with "only" 423 yards against San Diego while converting 31- of-40 passes.
"We stalled a little in the third quarter, but overall I thought we moved the ball pretty well, again, against a good defensive group," said Patriots head coach Bill Belichick.
Green-Ellis gained 70 yards on 17 carries for New England (2-0), which has yet to lose a home opener at Gillette Stadium. The facility opened prior to the 2002 season.
Philip Rivers recorded 378 yards on 29-of-40 passing, but committed three of San Diego's four turnovers.
Vincent Jackson had 172 yards and two touchdowns on 10 receptions for the Chargers (1-1), who outlasted Minnesota last week.
New England's first drive of the game began from its own eight-yard line. The Patriots converted a trio of third downs, and Brady capped the 12-play march with a 14-yard scoring strike to Aaron Hernandez.
San Diego quickly countered when Ryan Mathews scampered for a 10-yard TD run.
New England's next possession bled into the second quarter and stalled at the Chargers' four. A 22-yard Stephen Gostkowski field goal put the Patriots up 10-7.
Last week, Brady and Wes Welker connected on a 99-yard touchdown pass, tying the NFL record for the longest play. The duo didn't hook up this time, but Brady did orchestrate a 10-play drive from the shadow of his own end zone. Gronkowski's first TD -- a 10-yarder -- capped the lengthy march and made it 17-7.
The Chargers moved into enemy territory again with under two minutes remaining before halftime. New England defensive tackle Vince Wilfork thwarted the potential scoring drive, hauling in a deflected pass for his first career interception. A pair of Brady throws to Branch set up Gostkowski's 47-yard field goal on the final play of the half.
After a scoreless third quarter, which included Rivers' second interception, Jackson reeled in a pass with one hand for a three-yard TD.
New England faced a 4th-and-four at the San Diego 49 on its next series and opted to keep the offense on the field following a knee injury to punter Zoltan Mesko.
Brady's pass to Branch fell incomplete, but Tolbert fumbled on the subsequent drive. Four plays later, Gronkowski came down in the end zone with a 17-yard touchdown with 8:40 left. A two-point conversion gave New England a 28-14 advantage.
San Diego needed only three minutes to move 80 yards in eight plays, and closed to within a touchdown on Rivers' 26-yard scoring strike to Jackson.
Green-Ellis sealed the win with a 16-yard TD run inside of two minutes.
The Chargers' final possession ended with Rivers fumbling.
"New England is obviously an outstanding football team and we didn't play well enough to come into this stadium and win today," said San Diego head coach Norv Turner.
New England set a team record with its 10th straight regular season game with 30 or more points...Brady recorded his 29th consecutive win as a starter in the regular season at home, extending an NFL record...The Patriots were the only team in the league to finish undefeated at home in 2010...Welker caught seven passes for 81 yards. He has registered at least one reception in 63 straight regular season games, tying Ben Coates' club record...San Diego converted 10-of-12 third downs...The Patriots racked up 504 yards of total offense to 470 for the Chargers.