Gray set up Sam Vokes for the opening goal after just two minutes at Turf Moor and then doubled Burnley's lead before half-time.
The striker cut inside and slipped a low left-footed shot into the bottom-left corner after great work by debutant Steven Defour, with Gray delighted to get off the mark for the new season.
"It feels unreal to score my first Premier League goal," Gray told Match of the Day.
"It's nice to do it early because the longer the games go without scoring it plays with your head.
"It was a great team performance. I don't think we deserved to lose last week and it was important to make it right this week.
"We know we're not going to out-play teams every week but we have the biggest heart."