Ferguson, back after a 14-month absence after being sacked at Preston, saw first-half goals from Brighton pair Chris Wood and Elliott Bennett put Gus Poyet's men in charge.
Wood's second arrived 10 minutes after the break, but Lee Tomlin reduced the deficit by heading in a cross from Craig Mackail-Smith and Brighton held off a late Peterborough fightback as both Chris Whelpdale and Grant McCann struck the crossbar.
Ferguson said: "I wouldn't have come back if I didn't think we could reach the next league.
"I've come back to the club with us high up in the table and we need some stability. I'm really looking forward to the challenge."
He added: "We needed a second goal and had one of those efforts that hit the bar gone in it would have been interesting."