The striker scored three times in the first 53 minutes at Turf Moor, with Ashley Barnes netting a penalty before Jermain Defoe replied for the visitors.
Burnley -- who have picked up 22 of their 23 points this season at home -- move nine points clear of their opponents after their seventh win lifted them to 11th.
The Black Cats' challenge unravelled early with injuries to Ivory Coast defender Lamine Kone and Nigerian striker Victor Anichebe proving fatal as David Moyes' side start the New Year in the relegation zone.
Already the scorer of a late winner against Middlesbrough on Boxing Day, Gray's latest heroics boost Burnley spirits ahead of a tough trip to Manchester City on Monday.
The 25-year-old, who was playing in the sixth tier of English football four years ago, threatened early before breaking through after half an hour following a mix-up by defensive duo John O'Shea and Papy Djilobodji.
He added two more in quick-fire succession on 51 and 53 minutes with Barnes converting the fourth from the spot on 67 minutes after Seb Larsson barged Scott Arfield in the box.
Defoe's 71st-minute consolation -- his ninth goal of the season -- prevented Sunderland's biggest defeat of the season.