Hibs thought that they had found a safe pair of hands in Brown when he replaced the error-prone Zibi Malkowski in the Easter Road goal with the start of the John Collins era.
But Brown proved he's still capable of making silly mistakes as he was caught off his line early on to concede the opening goal.
Charlie Adam curled his 35-yard free-kick just inside the upright, with the goalkeeper completely out of position, to take his tally for the season so far to nine goals.
The first half was marked by a series of robust challenges as the Hibs fans booed former captain Kevin Thomson every time he touched the ball.
Ivan Sproule received treatment after clashing with Ugo Ehiogu, while Alan Hutton was the victim of a poor challenge from Rob Jones although both players were able to continue.
The home side came to life in the last ten minutes of the game and won a dangerous free-kick right on the edge of the area. But David Murphy's curling effort was just wide of target and Rangers went into the break with a one-goal lead.
Hibs started the second half brightly with Abdessalam Benjelloun, on for Thomas Sowuni, adding an extra threat up front.
But, just as the Edinburgh side looked to set to break back into the match, disaster struck for goalkeeper Brown for the second time in the match.
Rangers won a free-kick on the edge of the area and Adam stepped up to take it again, this time sending it straight between the hapless goalkeeper's legs.
Hibs didn't give up and had chances to come back, including a blistering effort from Steven Fletcher which forced an excellent save from Allan McGregor, but they never looked like hauling back the Gers.