Gunners and England forward Walcott now has five goals in eight games, taking advantage of a heavy Jordi Amat touch for his first and a poor Jack Cork header for his second.

The Swans looked dejected after the quick-fire double, though Gylfi Sigurdsson pounced on a Granit Xhaka error to curl in and give them hope before the break.

Mesut Ozil volleyed an Alexis Sanchez cross into the top corner to restore a two-goal lead for the hosts, but substitute Borja tapped in from the impressive Modou Barrow's cross to set up a tense finale.

Arsenal saw Xhaka sent off for a petulant trip with 20 minutes left and dug in to earn a win which moves them level on points with league leaders Manchester City.

Walcott's purple patch

Defeat leaves Swansea in the bottom three, winless since the opening day and they have now equalled their worst start to a league season. But it would be wrong to be overly negative about this display.

They were competitive early on but two defensive lapses left them facing a deficit they almost clawed back.

Walcott was on hand from close range to punish them and he has now scored as many goals in eight outings as he did in all 28 of his Premier League appearances last season.

The 27-year-old has only ever reached double figures once in a league season, scoring 14 times in the 2012-13 campaign.

But he seemed hungry in front of goal, with six shots - a game high - and showed instinct to sense Amat would have difficulty dealing with a bouncing ball, allowing him to prod the opener.

Walcott's approach play was also sharp - completing 92% of his passes - and he worked hard too, with only Santi Cazorla and Hector Bellerin covering more ground for Arsene Wenger's side.

Late on he missed two one-on-one chances for his hat-trick, the first of which saw him strike the post and watch as the ball rolled agonisingly back across the goalline.

Walcott's late misses were among 16 Arsenal shots - but Swansea managed 13 themselves.

In their previous away fixture against Southampton in September, they managed just six, so there was an undoubted intent on show in Bradley's first game.

The Premier League's first American manager has talked of a "fresh start" for everyone at the club.

Barrow, who has been out on loan twice since joining in 2014, clearly sought to impress as he constantly outwitted Nacho Monreal to deliver crosses, most notably when picking out Borja who finished from 10 yards.

His energy and drive perhaps summed up Swansea's spirit. Yes, they look at risk in the bottom three - but in acting early in the campaign, the club's hierarchy have given Bradley plenty of time to right things.

He may not have been able to match former Swans managers Michael Laudrup, Garry Monk and Francesco Guidolin in winning at Emirates Stadium, but the visiting supporters should leave with optimism.

Read: 'We can be a really good team' - Bradley

Xhaka was Arsenal's main negative during what was at times a thrilling encounter. His error for Sigurdsson's excellent finish gave Swansea a footing, his late kick on Barrow almost put his side under more pressure than they could take.

Wenger said he would not appeal the dismissal but admitted it "made it difficult for us" after watching his goalkeeper Petr Cech save headers from Leroy Fer and Federico Fernandez late on.

The erratic display by his £35m signing may prompt concern, but Wenger should be pleased to see what he called "good solidarity" to hold on for the win.

The recent international break marked 20 years at the club for the Frenchman. With his contract up in the summer, how many more chances will he have to guide Arsenal to their first title since 2004?

His side have trailed for just 52 minutes in the league this season. They have been solid and when questioned by Swansea they found the grit which will undoubtedly be needed if they are to end their title wait.

Man of the match - Theo Walcott

What they said...

Arsenal manager Arsene Wenger: "I have some mixed feelings because it looked at some points comfortable and then it never was.

"We have the same number of points as Manchester City so it's down to us to continue.

"If you look at the game the potential is very interesting but we have to be intelligent enough to improve."

Swansea manager Bob Bradley: "That game had many different parts. We started poorly.

"Defensively the first two goals were not handled well, but we gave ourselves a real chance.

"We are confident we can turn this around. After the week of training we have just had and the mentality of the team, for me we are going to become a good team."