Arsenal had gone ahead through Bukayo Saka's own record-setting goal, before Virgil van Dijk equalised nine minutes later.
Mikel Merino then scored what the Gunners thought would be the winner as the game ticked into the final minutes at 2-1.
But Trent Alexander-Arnold's beautiful ball over the top near the end of the game was picked up by Darwin Nunez who unselfishly passed it to Salah.