There were also victories for Hull and Stoke on Saturday afternoon as they, like the Gunners, hit back successfully following opening weekend losses.
Arsenal came under fire from their fans following last weekend's 3-1 home loss to Aston Villa but they bounced back with a 3-0 Champions League defeat of Fenerbache in midweek and picked up their first league points at Fulham.
Olivier Giroud netted for the third successive game to put Arsene Wenger's men in front after 14 minutes and a brace from Lukas Podolski (41 and 68) extended the lead in the lunchtime kick-off.
On-loan Aston Villa striker Darren Bent netted on his first Fulham appearance to pull a goal back for the hosts in the 77th minute, but Arsenal had already done enough for the points.
In one of the five 3pm kick-offs, Stoke recovered from a half-time deficit to beat promoted Crystal Palace in Mark Hughes' first home match in charge at the Britannia Stadium.
Marouane Chamakh's first Premier League goal since 2011 put Palace ahead in the 31st minute but Stoke turned the game on its head with two goals in quick succession after the break.
Charlie Adam drew the teams level in the 58th minute and then four minutes later Ryan Shawcross slammed home the winning goal for Stoke.
Palace's fellow top-flight newcomers Hull survived the 27th-minute dismissal of Yannick Sagbo to defeat Norwich 1-0 at home.
Robbie Brady's 22nd-minute penalty, given after former Tiger Michael Turner pulled down Sagbo inside the area, put Hull ahead but the hosts suffered a blow soon after when Sagbo was handed a straight red card for an off-the-ball incident.
However, Norwich could not make the most of their numerical advantage as Steve Bruce's men recovered from their 2-0 loss at Chelsea with a three-point haul.
Sunderland, who started their season with a home loss to Fulham, were within minutes of celebrating an opening victory themselves only to be denied by a late Jose Fonte equaliser at Southampton.
Summer signing Emanuele Giaccherini, standing only 5ft 6in, headed home a Sebastian Larsson corner after just three minutes to give the Black Cats the lead at St Mary's Stadium but Fonte's 88th-minute leveller saw the points shared.
The other two Premier League matches failed to produce a goal, with Everton being held at home by West Brom and Sam Allardyce's West Ham getting a point from the trip to his former club Newcastle.
In the late kick-off, Liverpool beat Aston Villa 1-0 at Villa Park.
Daniel Sturridge proved Liverpool's match-winner for a second successive weekend as the Merseyside club edged out Villa to make their best start to a Premier League season for five years.
The Birmingham-born striker, who started his youth career with Villa, delivered a moment of pure quality midway through the first half, receiving Jose Enrique's left-wing pass before dancing past two defenders, rounding Brad Guzan and transferring his balance to poke home with his left foot.
It came after the England marksman fired the Reds to a 1-0 opening-day win over Stoke, leaving Brendan Rodgers' side with six points from their first two league games for the first time since 2008.
Saturday's Premier League Results
Fulham 1-3 Arsenal
Aston Villa 0-1 Liverpool
Everton 0-0 West Brom
Hull 1-0 Norwich
Report | Reaction
Newcastle 0-0 West Ham
Southampton 1-1 Sunderland
Stoke 2-1 Crystal Palace
Sunday's Premier League Fixtures
Cardiff vs Man City
Tottenham vs Swansea