Club record signing Mesut Ozil starred on debut for the Gunners, setting up the opening goal for Olivier Giroud, with a classy touchy and quality ball for the Frenchman to sweep home in the 11th minute.
The German playmaker was also the orchestrator of some more killer balls, particularly on two occasions to Theo Walcott, who was unable to finish.
Sunderland hit back early in the second half when Craig Gardner converted from the penalty spot after Laurent Koscielny, for the second time this season, was penalised for a tackle in the box this time on Adam Johnson.
In the 67th minute, Gunners midfielder Aaron Ramsey fired home a spectacular volley from just inside the area to restore the lead before the Black Cats were cruelly denied another leveller when Jozy Altidore outmuscled Bacary Sagna to slot past Wojciech Szczesny but referee Martin Atkinson called a free-kick without paying advantage.
In the end, however, Arsenal set up a two-goal lead when Ramsey netted a second from close range after good lead-up passing from Ozil and then Giroud.
The Icelandic attacking midfielder opened the scoring in the 28th minute when he received a clever ball from debutant Christian Eriksen before doubling the home side's advantage five minutes into the second half by thumping home a back post ball from Paulinho from close range.
Robin van Persie netted his third of the campaign on the stroke of half-time when he sent Julian Speroni the wrong way from the spot after Kagisho Dikgacoi was sent off for denying Ashley Young, who had earlier been booked for diving, a clear goalscoring opportunity.
£27.5million signing Marouane Fellaini almost scored a brilliant goal after coming on for his debut in the second half but it was Wayne Rooney who added a second, scoring with a curling free-kick in the 81st minute.
Elsewhere, Newcastle United made it two in a row by beating Aston Villa 2-1 away with Hatem Ben Arfa and Yoan Gouffran on the scoresheet while Christian Benteke netted his fourth of the season for the losing side.
Everton surprised Chelsea with a 1-0 result at Goodison Park thanks to Steven Naismith's first-half header, Gareth McAuley scored an injury-time equaliser for West Bromwich Albion who denied Fulham 1-1 at Craven Cottage and Cardiff City held Hull City to a 1-1 draw at the KC Stadium.
Stoke City extended their unbeaten streak to three matches when they held Manchester City to a 0-0 draw at the Britannia Stadium which was the same scoreline in West Ham United's trip to Southampton on Sunday.
2013/14 Barclays Premier League scores