The Gortnahoe man, who came into the team in place of the injured Graziano Pelle, netted after 55 and 90 minutes and was named Man of the Match by BT Sport pundit Robbie Savage.
Southampton are 12th in the Premier League table after securing the three points against an Arsenal side hoping to leapfrog Leicester City in the title race.
The Saints next match is away to West Ham on Monday.
