Waddecar's first came from the spot after there was a handball in the area, before Brig's number seven added a second late on with a good finish into the roof of the net.
Joey Collins made five changes from the side that lost to Nantwich in the FA Trophy on Tuesday, with debuts given to on-loan Chester midfielder Louis Hayes and forward James Dean.
Dean was quickly into the action, his attempted backheel going narrowly wide of the post on five minutes.
Although Brig were putting plenty of pressure on their hosts, chances were at a premium in the opening half hour.
Waddecar was unlucky not to give the hosts the advantage on 30 minutes when his well-struck right footed shot was well saved by Stafford 'keeper Lewis King.
Hayes then floated the ball into the box and onto the head of Dean shortly before half time but the Brig debutant's effort went into the 'keeper's gloves.
Stafford had the better of the start of the second half, Will McGuffie breaking free from a corner and hooking the ball over the bar.
Daniel Burns then headed a subsequent corner wide from six yards out.
Burns was soon in the action at the other end when he handled Dean's knockdown in the area, referee John Mulligan pointing the spot.
Despite King guessing the right way, Waddecar struck a hard and low penalty underneath his dive to give Brig a deserved lead on 60 minutes.
And Brig, seemingly inspired by that goal, kept on pushing and Hayes did well to find himself free on the edge of box before hitting his effort over the bar.
The visitors then came close, a goalmouth scramble from another Stafford corner ending with the ball being struck over the bar from close range.
Brig continued to find themselves with men free on the counter as Stafford pushed forward, Dean unlucky not to see his attempted chip go in after running clean through past the defence.
The impressive Dean, given the man of the match award, had an important part to play in the second goal, his lay off allowing Waddecar to fire the ball into the roof of the net on the edge of the box to spark wild celebrations behind the goal.
The win takes Brig out of the bottom three and on to 12 points, with Stalybridge Celtic the next team to visit the Sir Tom Finney Stadium next weekend.
Match photos: Full gallery of match photos available here: https://flic.kr/s/aHsmJ8L6r8