Pepe, who arrived at the Emirates Stadium on a club-record deal in August, scored his first Premier League goal as the Gunners fought back to defeat Dean Smith’s men at home.
With the Gunners trailing 1-0, Matteo Guendouzi won a penalty for the hosts after he was brought down in the area and the Ivorian forward stepped forward to convert from the spot in the 59th minute.
At the end of the game, Emery confirmed Aubameyang as the designated penalty taker in the team and expressed his delight with the Gabon forward’s gesture to allow Pepe to open his goal account for the club.
"Yes, it's Aubameyang who is responsible for penalties. Also Lacazette, and today for me is a very big decision from Aubameyang to let Pepe shoot to give him confidence and the possibility to score,” Emery told the club website.
"Really, the responsibility is Aubameyang and I was happy when I saw that decision from Aubameyang.
"He is hungry every day to score, to achieve, individual and collective objectives. Today that decision shows a really great player."
Late on in the encounter, Aubameyang completed the comeback for the Gunners with his well-struck free-kick in the 84th minute to give Unai Emery's side their third Premier League win of the season.
Pepe will be hoping to build on his maiden Arsenal goal when they take on Nottingham Forest in a League Cup fixture on Tuesday.