Goals from Sam Togwell and Garry Thompson set up the victory, which moved the Iron up to 18th in the League One table and kept them two points ahead of the final relegation spot.
While no one at the club is under any illusions about the size of the task ahead, Brass was delighted to open 2012 with three points having failed to claim victory in their last nine games of 2011.
“It's a relief. We are fully aware of our position in the table and where we are at," said Brass.
"But in football it turns quickly and to the boys put in a very good performance on the back of a decent one at the weekend.
"You have to go that extra yard in football at every level and they did that. They have to believe in themselves and it's a long haul to get where we want to be. Performances like that set the standard and set you up.''
Hartlepool have now lost nine consecutive home games, and for recently-installed boss Neale Cooper it was not the glorious homecoming he wanted for his second spell in charge of the club.
"Our overall performance was second best, missing out on second balls in the middle of the park and the players should enjoy playing here in front of a big crowd," he said.
“It was too easy for them to get balls into their strikers and we didn't do it. We were very much second best to everything, we nearly got there, nearly did something – not good enough and too slow.
“I've seen things to work on and we need pace. We have to be sharper and quicker in moving the ball."