A 52nd-minute effort from Aston Villa midfielder Fabian Delph following a quick counter-attack beat Arsenal goalkeeper Wojciech Szczesny but struck the inside of the right-hand post and rolled across the line.
GDS came into play as television replays shown in the press box showed the referee Anthony Taylor had been notified that the ball did not cross the line at any point.
The system was used for the first time in English football during the Community Shield last Sunday.
Premier League chief executive Richard Scudamore said earlier this month that there were 31 occasions last season where the system would have been helpful - three of those ended up with incorrect decisions.
He added: ''It's a very exciting development in world football. 'It is a goal decision system - it is no longer just goal-line technology.''
Source: PA
Source: PA