"I'm very happy!" said beaming Bees boss Brennan afterwards. "A great team performance and another winner from Browney.
"Would I have taken a point before the game today? Probably but we've got players that will go to the line and get that bit extra.
"It's got nothing to do with me, it's the players, I just pick them. We've got some real leaders out there.
"It just epitomises what we're all about. We were up against it with some players being out but what a great showing from our so-called fringe players."
The visitors started well, with Lee Ndlovu leading the assault for Brennan's men.
And Ndlovu showed his quality on 15 minutes, beating two defenders and feeding Browne in the area but his low effort was smothered by Rob Lainton in goal for Alty.
And on the half-hour mark, a long-range diagonal ball by Anthony Hartigan was headed down by Billy Clifford at the far post but Ndlovu somehow fired over from inside the six-yard-box.
At the other end, Matty Kosylo's cross was headed onto the underside of the bar by top scorer Regan Linney, with the ball landing agonisingly on the line and then bouncing clear.
But the visitors rightly got their noses in front a minute from the break, when Browne headed in Hartigan's free-kick at the near post for his second goal in as many matches.
The hosts improved after the restart, with Charlie Olson volleying wide from close range and Kosylo and Linney both firing wide from distance ...