The visitors took the lead through Paul Mullin only to be pegged back by Asa Hall's acrobatic effort before half-time.
But Gornell pounced in the 55th minute and Accrington survived a late onslaught from the hosts to claim the win.
John Coleman's men made the most of a nervous Luton start to take the lead in the 16th minute.
On-loan defender Harry Worley failed to clear his lines contriving only to head the ball straight to James Ryan who, from the byline, squared for Paul Mullin to tap home from a yard out.
The Hatters reshuffled early on as new signing Wayne Andrews replaced Garreth O'Connor in the 23rd minute and the former Coventry man's introduction sparked the hosts into life.
Another new recruit, Tom Craddock from Middlesbrough, fired into the side-netting when well placed on the half-hour mark, but the equaliser arrived four minutes later.
Jake Howells' cross from the left didn't appear to cause any immediate danger, but Hall acrobatically swivelled to hit a superb volley over his own head and over visiting goalkeeper Kenny Arthur and into the top corner.
Hall had a chance to get a second seven minutes from half-time, but this time didn't prove to be as accurate as he volleyed over right-footed from 12 yards after Michael Spillane's cross from the right.
Just like the first half, Luton started the second period slowly and the visitors almost went ahead in the 51st minute when Paul Mullin's flick-on released Gornell only for Conrad Logan to smother at the striker's feet.
Gornell did find the net four minutes later, however, as another Paul Mullin header, this time after a free-kick from brother John, found his forward partner and Gornell even had time to bring the ball down on the edge of the six yard box before firing into the roof of the net.
Luton rallied late on and a mazy run from Craddock in the 84th minute ended with a cross-shot that was prodded wide by Andrews from six yards.
The Hatters thought they had earned a point a minute from time when the ball dropped perfectly for Hall in the area, but Arthur somehow kept out the midfielder's driven effort.