But the Black Cats were left to rue a host of missed chances to move further clear of the drop.
In an even first half, both sides had penalty appeals turned down while Patrick van Aanholt hit the woodwork with a free-kick for the hosts and Vito Mannone saved well from Alexis Sanchez.
Ater the break Sunderland were left frustrated by Arsenal keeper Petr Cech.
The 33-year-old produced a fine double save to deny Jermain Defoe and Yann M’Vila before tipping Wahbi Khazri’s low shot around the post.
Defoe then saw a lobbed effort go wide with Cech stranded before Laurent Koscielny cut out the striker’s pass across goal which would have left Fabio Borini with a tap-in.
Jack Wilshere made his first appearance of the season after a broken leg, coming off the bench for the final six minutes.
In the closing stages it was Arsenal who went closest to finding a winner but Mannone denied Sanchez again to ensure his side claimed a potentially vital point.