The in-form Thomas' early opener - his sixth goal so far this term - was followed up by his seventh shortly after as Gary Liddle's side turned in a fluent, impressive first half showing to put the game beyond the hosts at the SFC Stadium.
The result lifted the Seasiders to tenth place in the Pitching In Northern Premier League Premier Division - just seven points shy of a top five spot.
In a remarkable one-sided first half, the hosts would not have been able to feel hard done by had the Seasiders netted more than their two strikes.
It took just over six minutes for the first goal to arrive, with Oliver Thompson spraying a pass out to Thomas on the left. His effort was initially blocked but he was able to poke the ball into the net with his second bite of the cherry.
It could have been more. Stephen Walker couldn't find the target after Shane Bland had picked him out with an exquisite kick, before Layton Watts struck wide following another brilliant ball from Bland.
Just before the 25-minute mark, Liddle's men had a second. Great work from Oli Thompson who let the ball run across his body before beating his man and giving it to Watts. Watts found Thomas, who took the ball on his thigh and drilled it into the bottom corner.
The pressure continued, with Thompson striking over from close range and Walker lashing wide from a tight angle.
The best it got for Bamber Bridge in the first half was an effort from distance from Michael Potts which didn't trouble Bland.
After the restart, there was a reaction from Brig. Liam Brockbank's attempt from range was well saved by Bland, while Christopher Churchman forced the Whitby gloveman to react with a free-kick.
Whitby always posed a threat on the counter-attack, largely carried through Thomas who, just ahead of the hour mark, drove forwards before being upended. Searching for a hat-trick, his free-kick drifted wide of the mark.
Substitute, Matthew Tymon, squandered the opportunity to net his first goal since his return from Bishop Auckland. After the ball was worked well into the path of Walker, he found Watts who, in turn, picked out Tymon at the back post, however the striker struck high over the crossbar from six-yards out.