The Gunners forced Nick Pope into a number of saves, but their hopes of sealing a first Premier League win since the victory over Manchester United on November 1 were hit when Xhaka was dismissed shortly before the hour mark for grabbing Ashley Westwood by the throat.
Their misery was compounded in the 73rd minute when Pierre-Emerick Aubameyang headed into his own net from Westwood's corner, to the dismay of 2,000 returning Gunners supporters.
Arsenal, who have now lost four consecutive top-flight home games for the first time since December 1959, remain in 15th with 13 points, while the Clarets move up to 17th place.
Full time in north London. #ARSBUR— Arsenal (@Arsenal) December 13, 2020
The hosts made 10 changes from the side that beat Dundalk in the Europa League on Thursday, and started slowly. They should have fallen behind after 13 minutes, but an unmarked Chris Wood inexplicably headed wide from eight yards.
Rob Holding headed over at the other end, while Alexandre Lacazette was denied by the leg of Pope after being picked out inside the penalty area by Kieran Tierney.
The Burnley goalkeeper denied Tierney and Bukayo Saka in quick succession at the start of the second period before Xhaka's moment of madness.
The Switzerland international's initial caution for pawing at Westwood was upgraded to a red card by referee Graham Scott after he viewed the incident on a pitchside monitor.
That was the sixth Premier League red card for the Gunners since manager Arteta took over in December 2019 – double that of any other side in the same period.
Mohamed Elneny was fortunate not to also receive his marching orders soon after, Scott deciding his push on James Tarkowski warranted just a yellow card.
Arsenal's reprieve did not last long, though, Aubameyang glancing the ball past Bernd Leno to guarantee an uncomfortable few days for Arteta.
What does it mean? Arteta's faith in faltering players not repaid
Arteta said he had "zero doubts" his side would respond to last weekend's north London derby defeat to Tottenham, but the Spaniard is left to rue another costly setback against a side that started the day in the bottom three.
They were not entirely terrible, carving out 19 shots and enjoying almost 65 per cent of possession, but that will be of little comfort to Arsenal fans, who ultimately saw their side suffer a seventh Premier League defeat of the season and a first ever home loss to Burnley in the competition.
Westwood stars for Clarets
The former Aston Villa midfielder was superb in the middle of the pitch, creating the game's only goal with a teasing corner, making a team-high three key passes and putting in seven crosses – more than any other Burnley player.
Xhaka stupidity costs Gunners
Xhaka has had his very public issues with Arsenal supporters and he can expect to be in their bad books again after a pitiful display. There can be no arguments about his red card, which ultimately proved to be the catalyst for another miserable defeat.
Key Opta facts
- Burnley may not have beaten Arsenal in the Premier League before Sunday's success, but it was a different story in the days of the old First Division. This was the Clarets' first league win in their rivalry since September 1974, ending a 15-game barren run (D4 L11).
- Arsenal’s tally of 10 goals after 12 Premier League games is their lowest at this stage of a top-flight season since 1981-82 (8 goals).
- Arsenal have received six Premier League red cards since Arteta’s first game in charge in December 2019, double that of any other side in this time.
- Since Xhaka’s Premier League debut in August 2016, only Fernandinho (4) has received more red cards in the competition than the Swiss midfielder (3).
- Aubameyang’s own goal was the first time Arsenal have conceded via a set-piece this season, becoming the 20th and final team to do so in the Premier League.
Arteta will hope to still be in charge when the Gunners host high-flying Southampton on Wednesday, while Burnley visit Villa a day later.