Hugo Lloris got down low to keep out the substitute’s poor kick and rescue a below-par Tottenham who had equalised in the 74th minute through Harry Kane’s penalty kick.
Arsenal, bidding to close the gap to their arch-rivals to one point, had taken the lead in the 16th minute when Aaron Ramsey broke clear after a mistake by Davinson Sanchez.
Kane had a first-half header ruled out for offside, but Tottenham struggled to create chances as a third English Premier League defeat in succession for the first time since 2012 loomed.
Alexandre Lacazette had wasted a good chance to make it 2-0 to Arsenal, but it was the man who replaced him, Aubameyang, who cost his side victory.
The Gabonese hit a poorly-struck penalty kick after Sanchez was adjudged to have fouled him.
A niggly game ended with Arsenal’s other substitute Lucas Torreira being red-carded for a high tackle on Danny Rose.
Tottenham’s first league draw of the season left them third on the table, four points above Arsenal.
Arsenal themselves can be overtaken by Manchester United if they beat Southampton later in the day.