This result leaves Arsenal five points behind leaders Manchester City and four points adrift of second-placed Liverpool.
Liverpool entered the weekend at the top of the table, having won 11 of their first 12 matches in all competitions under manager Arne Slot.
However, the draw means the Reds now sit one point behind Manchester City, while Arsenal remains in third place, five points off the lead.
Bukayo Saka made his return from a hamstring injury to start for Arsenal, giving the home team an ideal beginning with a remarkable touch and finish from Ben White’s assist in the ninth minute.
Virgil van Dijk quickly equalized from a corner, but Arsenal regained the lead before halftime with a header from Mikel Merino.
Liverpool showed improvement in the second half and were rewarded when Darwin Nunez set up Salah for his eighth goal of the season.