With just 24% possession and a single shot on target, which arrived inside the first 10 minutes, the Clarets were made to defend doggedly in North London.
But they went about their business rather diligently against the Gunners and restricted the hosts to just five shots on target across the 90 minutes.
Nick Pope saved with his legs to deny Martin Odegaard and preserved a fourth clean sheet of the campaign with a fine stop to keep out Emile Rowe Smith's effort inside the box.
Alexandre Lacazette somehow missed the target late on when nipping ahead of Ben Mee to meet Smith Rowe's pull back, but the French striker flicked the ball wide of the upright.
Mikel Arteta's side, however, didn't have it all their own way as Dwight McNeil threatened on several occasions.
The ex-England Under 21 international's cross-shot was tipped over the bar by Aaron Ramsdale in the first half, the winger's low effort was turned for a corner in the second while a late attempt just cleared the crossbar.
1. Nick Pope 8
The goalkeeper's save from Smith Rowe in the second half was the pick of his highlight reel, but he also made a smart save with his legs to deny Odegaard before the break. A fully deserved fourth clean sheet of the campaign.
Photo: Stu Forster
2. Connor Roberts 7.5
Looked every bit a Premier League player on his first ever start at this level. Stood his ground when Martinelli attempted to weave his way into the penalty area, switched well with Lennon when Tierney provided the overlap, and looked comfortable on the ball.
Photo: Catherine Ivill
3. Erik Pieters 7
The Dutchman did ever so well considering he was up against one of the brightest young talents in English football on only his second start of the season. Stretched by Saka throughout, beaten by his quality on occasions, but did all he could to prevent the winger from hitting the byline.
Photo: Catherine Ivill
4. James Tarkowski 8
Shown a clean pair of heels when Smith Rowe burst into the box from the left hand side to tee up Lacazette in the second half, but back to his best otherwise. Proved to be impermeable when the hosts had the ball in central positions in the final third and cleared everything that came into the box.
Photo: Ryan Pierse