After the hosts had taken an early lead, Brig hit back through Alistair Waddecar.
However, they were unable to add to that and were sunk by a late penalty converted by Dale Hopson.
Whitby opened the scoring in the fourth minute through Junior Mondal with the first attack of the match.
But Brig responded and Brad Carsley headed against the post after a great run and cross by Andy Haworth.
Preston North End's predicted line-up for Championship visit of Rotherham United
Preston-born Clarets legend Lenny Johnrose dies at 52
John Smith's PNE Fans' Panel verdict: Sunshine all the way
Luton Town boss says best team didn't win after Championship defeat to Preston North End
Preston North End showed the hallmarks of a successful side as they beat Luton Town
A few minutes later it was Haworth who was denied by the woodwork as his 25-yard shot crashed against the crossbar after it took a deflection.
The visitors were soon rewarded for their good work when in the 22nd minute Ryan White set-up Waddecar who curles the ball home.
Oli Byrne in the Brig goal pulled out a spectacular goal, while in the second half Danny Forbes, Carsley and Paul Dawson were all denied.
The sucker punch arrived 11 minutes from time after a foul by Byrne and Hopson made no mistake from 12 yards.
Elsewhere, Lancaster drew 1-1 with Basford, Clitheroe lost 2-1 at home to Trafford and Kendal Town were bedaten by the same scoreline against Runcorn Linnets.