Pearson is currently searching for a full-time replacement for sacked boss Phil Parkinson but Brown would do his own cause ho harm by picking up another three points on Saturday.
Brown said in the YEP: "It will be a pressure-cooker game, there's no doubt about that. We'll have 3,000 fans at Leeds on Saturday and that's what we're looking for, everyone to get behind the team to produce the end result.
"It's a big, big derby for us and whoever wins it will go a long way to getting out of the bottom three. We're expecting a tough game but we feel that we've prepared properly for it."
Brown, who managed Derby for seven months before being fired in January, is not surprised by Leeds' current situation at the bottom end of the Championship.
He added: "I'm really not shocked by anyone's position in this league. If you don't win matches you're in a relegation scrap, it's as simple as that.
"Football holds no respect for big clubs whatever city they're from and we've all been in this position before.
"There have been some massive clubs in this predicament and Leeds are just the latest in a long line."