Alexis Sanchez put the Gunners ahead when he got in front of defender Lamine Kone to head in Alex Oxlade-Chamberlain's cross.
The dominant visitors had a strong penalty appeal turned down after Sanchez looked to have been brought down before Jermain Defoe equalised from the spot after keeper Petr Cech had fouled Duncan Watmore.
However, Arsenal reasserted their authority and lead with three goals in six minutes and 20 seconds.
Olivier Giroud came off the bench to guide in a shot and then headed in a Mesut Ozil corner, while Sanchez's close range effort was the signal for the home fans to start streaming out of the Stadium of Light.
The win moved Arsenal top of the Premier League - but whether they stay there depends on how Manchester City and Liverpool fare in their later games.
Arsenal boss Arsene Wenger wanted a win in the early Saturday game to put pressure on his side's rivals and his players duly delivered.
The Gunners were missing the in-form Theo Walcott, but Oxlade-Chamberlain, who scored twice in the midweek EFL Cup win over Reading, competently filled the void.
He provided the cross for Sanchez, starting up front instead of Giroud, to head in the opener and the England midfielder has now been involved in seven goals in his past eight games in all competitions, with four goals and three assists.
Ozil had a chip saved when clean through and the Gunners were punished for failing to turn their dominance into further goals when Defoe equalised.
However, Arsenal regrouped and recovered with a late burst of goals and are unbeaten in 14 matches.
Arsenal were still smarting from referee Martin Atkinson not awarding them a penalty for Kone appearing to pull back Sanchez when Defoe gave Sunderland hope.
Wenger sent on Giroud, who was playing his first league game since 24 September following a toe injury, and he scored with his first two touches of the game.
"I have been lucky today, I had great assists from my team-mates," said France striker Giroud, who has scored seven goals in his last seven appearances against Sunderland in all competitions.
"It is a big time for me coming back from a tough injury and I'm very happy to be back on the pitch."
The latest defeat for Sunderland means they have made the worst ever start to a Premier League season, with just two points from 10 games.
Their fans might have feared the worst going into a game - and any concerns did not take long to be realised as centre-back Kone was caught on his heels for the opener, the sixth headed goal the Black Cats have conceded in the league this season.
That tally went to seven following Giroud's goal later on and the defending of Sunderland, who were using a seventh different back four combination under Moyes this season, left plenty to be desired.
Even when Defoe scored with the hosts' first shot on target, they failed to show the security in defence to build on that lifeline.
They had plenty of support with 44,322 at the Stadium of Light, but their capitulation left swathes of empty seats at the final whistle.
Sunderland manager David Moyes: "Once we get one or two of the injured players back, that will give us some more options and that will give us a better chance.
"The message is the players are giving everything they can. It was not through the lack of effort, or the lack of trying - they played a team with a lot of quality.
"We are not in a good position and need to play better. The players are doing their best, but you will only ever be judged by your results."
Arsenal boss Arsene Wenger: "It was a mental test when we were at 1-1. We missed so many chances, so many opportunities, and I was worried we could lose - but we have shown great strength to bounce back.
"In the Premier League at 1-1 you can lose the game but it was about how we responded. Do we panic, give up, feel sorry for ourselves? We responded well and in the end it was a comfortable win.
"It was an important result for us. We had six wins, then one draw at home, which was disappointing, and a second draw or defeat would have been like we had dropped our level."
On his introduction of Giroud, who then scored twice in the next seven minutes, Wenger added: "The manager has an easy credit when he has quality players on the bench and you don't need to be a special manager to make this decision. It was 1-1 and we had Giroud on the bench."
Arsenal travel to Bulgaria to play Ludogorets Razgrad in a Champions League group game on Tuesday before hosting north London rivals Tottenham in the Premier League on 6 November.
Sunderland are at Bournemouth in the Premier League on 5 November. AGENCIES