Brighton coach Graham Potter gave Mooy his first start for the club, with the Socceroo playing the full 90 minutes.
The midfielder was an unused substitute for the Seagulls in the weekend Premier League defeat to Southampton, after debuting for the club in their second round draw against West Ham United.
Potter made 11 changes from the loss to the Saints, including fellow Aussie Mat Ryan omitted from the squad for the EFL Cup clash.
Aaron Connolly gave the visiting Premier League club the lead on 55 minutes, before Tom Nichols gave Rovers an unlikely equaliser.
But Brighton had the last laugh - with Murray scoring in the second minute of added time to seal the win.
Discussing his side's performance, Potter said: "It was a really pleasing evening for us".
"It was a tough game. Bristol Rovers made it difficult for us and you'd expect that.
"But overall, the application and effort from the players was really pleasing.
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