The midfielder, signed from Strasbourg last summer, scored one and had another deflected into the net during a commanding first half on Monday (Tuesday AEDT).
Chemsdine Talbi completed the scoring for the Black Cats.
Sunderland's unbeaten home run was extended to 12 games - a record for a promoted side - and the team moved above Fulham and Everton into eighth place in the standings.
There was a healthy dose of fortune about Diarra's ninth-minute opener, as his right-foot shot took a nasty deflection to wrong-foot Burnley goalkeeper Martin Dubravka.
The touch was later given as an own goal by Axel Tuanzebe, making him the 12th player in Premier League history to score three own goals for three different clubs (Manchester United, Ipswich Town and Burnley).
However, there was nothing lucky about Diarra's second, which he fired from almost exactly the same position 23 minutes later. Dubravka got a hand to the fierce shot but could not stop it.
Talbi added the third after cutting in from the left and unleashing a superb shot.
Burnley did not have a shot on target and ended the night second-to-last on the ladder.
Scott Parker's men have not won in 15 league games since October. The Lancashire side were seven points clear of last-placed Wolves but five behind West Ham and nine adrift of fourth-from-bottom Nottingham Forest.
16°C