And it was a great goal too, Briscoe racing in to meet a cross from Paul Cook and send a header beyond Darren Ward in the 27th minute.
Ward had already made a point-blank save from Gareth Taylor while Robbie Blake had an effort disallowed for offside.
Burnley's cause was helped by their former loan striker David Johnson missing two clear cut chances in the second half.
Johnson, who scored five times in eight games with Burnley last season, has already hit 20 this time around, but he somehow managed to blaze high over from 12 yards before failing to make contact when another chance came his way.
Apart from that Burnley were rarely troubled and but for Ward their victory would have been far more emphatic.
Ternent said: "It was a great win against a very good side courtesy of a smashing goal. It's been a tough week but the players did really well to show that they are capable of beating anyone.
"Our ambition is the top six and I think we can do it if we steer clear of injury and suspension problems."Forest boss Paul Hart said: "We took too long to get going and defended like schoolboys. It's difficult to know the reason why but sometimes the though of defeat can become an obstacle.
"We have worked hard to get up to third and are desperate to stay there, but maybe we let the position dictate too much."