The Swans tasted defeat in Bob Bradley's first game in charge as they went down 3-2 at Arsenal.
The five-goal thriller at the Emirates also conjured a red card, with the home side seeing Granit Xhaka sent off with 20 minutes to go.
Arsenal led 2-0 after 32 minutes through a Theo Walcott double, but Gylfi Sigurdsson pulled one back with a sublime finish before the break.
The goals kept flowing, and Mesut Ozil's quality volley looked to have given Arsenal the points.
But the Swans kept plugging away, and Modou Barrow's pace was a key asset.
The Gambian then set up sub Borja, who scored his first for the club, to make it 3-2 before Xhaka's dismissal for hauling down the winger.
The Swans probed for an equaliser, with Barrow and Sigurdsson spurning great chances.
Walcott later hit the crossbar in added on time as he missed out on a hat-trick.
But the Swans were left point-less from Bradley's opening game in charge, but there were plenty of major positives to take from the trip to North London.
Swans boss Bob Bradley made three changes to the starting XI.
Bradley became the first American to manage in the Premier League - and Europe's top divisions - as he led his side out at the Emirates.
From the team that took to the field against Liverpool before the international break, Neil Taylor and Federico Fernandez - back from a groin injury - returned in defence while Modou Barrow was handed his fifth top-flight start of the campaign.
Record signing Borja wzs included among the substitutes while Fernando Llorente (rib), Jefferson Montero (ankle) and Nathan Dyer (ankle) were unavailable.
ARSENAL: Petr Cech, Laurent Koscielny (capt), Alexis Sanchez (Alex Oxlade-Chamberlain, 82), Mesut Ozil (Kieran Gibbs, 82), Theo Walcott, Alex Iwobi (Francis Coquelin, 68), Nacho Monreal, Santi Cazorla, Shkodran Mustafi, Hector Bellerin, Granit Xhaka.
SUBS: David Ospina, Gabriel, Lucas Perez, Mohamed Elneny.
SWANS: Lukasz Fabianski, Kyle Naughton, Federico Fernandez, Jordi Amat, Neil Taylor, Leon Britton (capt, Borja, 60), Jack Cork (Ki Sung-Yueng, 71), Leroy Fer, Modou Barrow (Angel Rangel, 82), Wayne Routledge, Gylfi Sigurdsson.
SUBS: Kristoffer Nordfeldt, Mike van der Hoorn, Stephen Kingsley, Jay Fulton.
Arsenal were quick to apply their influence and the Swans were under the cosh early on.
Alex Iwobi was the first to try his luck at goal, but his effort was deflected wide.
The Gunners were at it again soon after, and only the woodwork saved the Swans as Shkodran Mustafi rose to meet Mesut Ozil's corner, but it rebounded back off the crossbar.
The Swans were making rare forays into the Arsenal half, and their first chance was a decent one as Modou Barrow and Kyle Naughton linked to set up Leroy Fer, but the midfielder fired just ovef from 18 yards.
But Arsenal were on the attack shortly after, and it took a great block from Leroy Britton to deny Granit Xhaka inside the box.
Arsenal did take the lead, however, after 27 minutes as Alexis Sanchez's chipped pass was headed along goal by Hector Bellerin, and when that bounced back off Jordi Amat, Theo Walcott slotted home from close range.
The Gunners went close to doubling their lead two minutes later, but Sanchez chipped over after latching onto a long ball.
But the hosts did manage to extend their advantage after 32 minutes. It came after Lukasz Fabianski had denied Bellerin from close range and deflected his shot for a corner. But the resulting delivery was not cleared by the Swans defence, and Walcott again tapped home from point-blank range
The Swans were seriously under the cosh, and they needed to get back into the game.
And, with seven minutes left of the half, the Swans pulled one back out of nowhere.
Gylfi Sigurdsson snatched possession off Xhaka, and the Icelandic international curled his 18-yard left-footed effort into the far corner past Petr Cech.
That goal injected further belief into Bob Bradley's side, and Sigurdsson went close to getting an equaliser when he latched onto Barrow's cross, but the Arsenal defence did enough to deflect the attempt wide.
Then, in the final seconds of added on time, a pinpoint Sigurdsson free-kick found the head of Jordi Amat inside the box, but he could only direct straight at Cech.
HALF-TIME: Arsenal 2-1 Swans
The action continued at a fast pace after the break, with Walcott being denied a hat-trick from Fabianski's low save.
But Arsene Wenger's side restored their two-goal advantage just before the hour mark as a fantastic cross from Sanchez found Ozil, and the German powerfully volleyed home from close range.
Bob Bradley made his first change as Borja replaced Leon Britton.
And the Spaniard had an instant impact as he pulled one back in the 66th minute - six minutes after being introduced.
It was a well-worked goal, with the lively Barrow using his pace to beat Nacho Monreal, and the Gambian's cutback found Borja, who coolly finished from close range.
It was scintillating stuff, but more drama was to come.
Barrow was giving Arsenal major headaches down the Swans' right flank, and the hosts were reduced to ten men when Xhaka hauled down the winger when he was on the break.
It gave the Swans further hope, and two big chances came their way.
First, Barrow got onto the end of Wayne Routledge's cross, but his weak header was easily collected by Cech.
Then he turned provider as he again left Monreal behind. Barrow crossed low for Sigurdsson, but he could only fire his 12-yard effort high over the crossbar.
Arsenal were under the cosh, but their quickfire counter attack was a constant threat. And they went within inches of a fourth - and Walcott's third - as Fabianski was saved by the post.
The Swans, though, were not done yet as Kyle Naughton's lofted cross was met by Fer, but he didn't get enough power on his header to trouble Cech.
Again the Swans pushed, and another cross - this time by sub Angel Rangel - reached Federico Fernandez, but Cech was there to collect.
Then, in added on time, Walcott struck the crossbar from close range as Arsenal went to clinch it.
But referee Jonathan Moss blew his whistle soon after as the Swans fell to defeat.