Simon Smith's side led early on when Phil Watson powered over and Tom Ratcliffe converted for a 7-0 advantage.
The sides then exchanged penalties, Ratcliffe again showing an accurate boot to put Scarborough 10-3 ahead.
Hosts Brods battled back, touching down in the corner and subsequently converting to even things up at 10-10.
Scarborough again took the lead heading into the break, quick thinking from skipper Matty Jones releasing Aussie James Perrett to touch down.
Ratcliffe this time missed the conversion and Scarborough led 15-10 at the interval.
Scarborough were guilty of over-playing after the break and Brods took advantage, eventually kicking over a penalty to give themselves hope of a comeback at 15-13.
The visitors then took control again and after putting in some great phases and forcing a line-out, despite the driving mall collapsing, two phases later the prolific Watson bundled over for his second try and Ratcliffe again converted for 22-13.
Once again though the hosts battled back into the contest and they barged their way over before converting to narrow their deficit to 22-10.
But back came Smith's promotion-chasing visitors, who won a penalty inside the home 22. They chose to take the scrum and are rewarded with a penalty try to move 29-20 ahead.
With conditions deteriorating on a heavy pitch, Brods enjoyed some good possession in their own half, but Scarborough turned over the ball and Perrett found a gap to cruise through and score under the posts.
Ratcliffe converted for a 36-20 lead for Scarborough.
The hosts weren't lying down and accepting defeat though, and after camping on the Scarborough line, a driving a line-out resulted in them going over for a try, which they converted for 36-27.
Scarborough were forced to do some more defending to keep the hosts at bay, but they did just that and clinched a potentially crucial 36-27 victory that keeps them firmly among the promotion mix-up at the top of the Yorkshire One standings.
DON'T MISS: Two pages of coverage from Scarborough RUFC, including coach Simon Smith's column and much more, in Thursday's Scarborough News.