The Gunners had won their last 11 meetings with Burnley in all competitions but Mikel Arteta's men did not do nearly enough to extend that run as they again failed to make up significant ground on the top four.
Although Arsenal spurned presentable chances of their own, they could consider themselves a little fortunate to pick up a point as Jay Rodriguez somehow contrived to hit the underside of the bar from five yards out with 12 minutes remaining, the ball coming down on the goalline.
Both teams remain on 31 points, 10 adrift of the top four and seven above the bottom three.
An unmarked Alexandre Lacazette headed wastefully off-target from Pierre-Emerick Aubameyang's cross as Arsenal started brightly, before the latter latched on to David Luiz's lofted ball over the top, only to screw a shot hopelessly wide of the near post.
Burnley were grateful for a superb last-ditch tackle from James Tarkowski on Lacazette when the forward looked set to score, but the hosts soon grew into the game as Arsenal's threat faded.
Either side of Nick Pope staying big to deny Aubameyang, Rodriguez's low 25-yarder tested Bernd Leno while the impressive Dwight McNeil and Jeff Hendrick each went close.
Burnley certainly carried the greater threat early in the second half, Tarkowski and Ben Mee both threatening from set-pieces prior to Jeff Hendrick heading a McNeil cross narrowly past Leno's right-hand post.
Aubameyang sent a header inches past the post from Lacazette's left-wing delivery in a rare moment of second-half danger for the hosts, but it was Burnley who came closest to a winner, Rodriguez failing to convert McNeil's knock-down when it looked easier to score.
What does it mean? Arsenal with so much work to do
Arteta clearly deserves time to make his mark, but it is staggering how far Arsenal have fallen. They have now won just two of their last 17 Premier League games - and only six all season. To say the Spaniard faces a big rebuilding job would be a major understatement.
McNeil shines again
As Arsenal's attacking stars failed to convince, Burnley's McNeil was the most dangerous player on the pitch, posing a constant threat with his pace and dangerous deliveries. It surely will not be long before the winger is the subject of serious interest from a bigger club.
Gunners mis-fire in attack
This was not a good day for Arsenal's starting front four. Lacazette and Aubameyang should each have scored inside the first 15 minutes, with the latter also heading wide late on, while Gabriel Martinelli was virtually anonymous and Mesut Ozil also struggled prior to his 63rd-minute withdrawal.
Key Opta facts
- Burnley remain winless in 12 Premier League matches against Arsenal (D2 L10), though they avoided defeat against the Gunners for the first time since December 2009.
- Arsenal are unbeaten in all competitions during 2020 (P7 W3 D4 L0) since losing 2-1 to Chelsea in their final game of 2019.
- Burnley’s last two Premier League draws at Turf Moor have come on February 2nd, drawing 1-1 with Southampton in 2019 and goalless today against Arsenal.
- Arsenal have won just six of their 25 Premier League games this season (D13 L6), their lowest tally after 25 league games in a season since 1912/13 (one win).
- No Premier League goalkeeper has more clean sheets than Burnley’s Nick Pope this season (9, level with Alisson and Dean Henderson).
- Arsenal are the first team in Premier League history to draw as many as 13 of their first 25 league matches in a season, and the first in the top-flight since Manchester United in the 1980/81 campaign.
- Arsenal have drawn four consecutive Premier League games for the first time since February 2009 (five in a row).
- This was only Arsenal’s second goalless draw in their last 84 Premier League games, also drawing 0-0 in December 2019 against Everton.
Both teams can enjoy a mid-season break prior to their next fixtures. Arsenal host Newcastle United in a fortnight's time, while Burnley travel to Southampton a day earlier.