Goals from Danny Crow and new signing Stuart Fleetwood saw Luton ease past their opponents, who resorted to strong arm tactics from near enough the opening whistle.
But home keeper Mark Tyler was relatively untroubled all afternoon, whereas Luton could and should have run out winners by a larger margin.
Brabin said: “I’m delighted with it, delighted with the performance, and I thought we thoroughly deserved it.
“I’m delighted with the clean sheet, at last,
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“I think a lots been made of that, but I thought we thoroughly deserved it and I thought 2-0 was flattering to the opposition.”
Brabin made four changes to the side that drew 1-1 with Stockport County, dropping full backs Curtis Osano and Ed Asafu-Adjaye, while both Adam Watkins and John Paul Kissock moved to the bench.
The boss said: “Curtis Osano stubbed his toe last week when we played Stockport. We thought it would have cleared up by now but it hasn’t.
“A break’s been ruled out, but he’s still in a bit of pain. I thought Keith Keane was outstanding last week at centre half, so we’ve had to put him in at right back and bring big Dean Beckwith back.
“We needed a little bit of an aerial threat, as they are a big physical side and with Jamie Hand coming in as well, I think he gives us that other bit of protection in the midfield.”
Fleetwood was given the nod upfront, and showed his nous in front of goal, nodding home Robbie Willmott’s corner for his first strike in Luton colours.
Brabin added: “He’s been what were looking for definitely, but Danny Crow and Amari Morgan-Smith have made it a little bit harder for me.
“That’s what I want though, a strong squad of players and a bench itching to get into the action.”