The Seagulls entered the contest seeking to return to winning ways after enduring a six-game winless run in the Premier League, and they got off to a poor start at the City Ground as Anthony Elanga headed the hosts into a third-minute lead.
However, Ferguson restored parity for Brighton just before the half-hour mark with a curling strike - his sixth of the campaign - before Pedro, who came off the substitutes' bench to replace the injured Ansu Fati, headed the visitors in front in the fourth minute of first half stoppage time.
Pedro then netted his second of the match from the penalty spot to put Brighton 3-1 ahead on the 58-minute mark, but the game gradually became nervy for the Seagulls and frustrations boiled over when VAR intervened to award Forest a penalty in the final 15 minutes following a coming-together between Callum Hudson-Odoi and Jack Hinshelwood inside the box.
Lewis Dunk was shown two yellow cards in quick succession for dissent before Morgan Gibbs-White covered the resulting spot kick to set up an enticing finish, but Brighton eventually held on to claim a hard-fought victory, sparking wild scenes from the visitors with Roberto De Zerbi running onto the pitch at full time to celebrate with the travelling supporters.
"It was a mad old game! It was worth it for the three points," Ferguson told BBC Match of the Day after the game.
"We've dropped points in those moments [after Lewis Dunk's red card] and today we came together as a team to push over the line.
"Every game there's an opportunity to impress and that is what I hope to do when I come in. The manager is very invested, really emotional and he can't help himself. He wouldn't just walk over to the fans and celebrate!"
Speaking to BBC Sport, Pedro added: "Great win today, a tough game. We did well and deserved to win.
"[Roberto] De Zerbi always says to be ready. I'm happy to help the team to win today. There are a lot of injuries, the group is strong enough to play and win.
"Now we must think about the Europa League. It was difficult at the end. We kept going and fought to win."
Reacting to the win and celebrations, Brighton boss De Zerbi told Sky Sports: "Our celebrations today, we didn't win the Champions League, we know that very well. But it was a tough moment for us. We want to celebrate this way with our fans, our attitude to win was great.
"I think we played one of the best games in our season in terms of the quality of the play and personality. We never suffered until the red card. Nothing else more or less.
"But honestly it's difficult to win the game for us, given we have ten players with injury and we finished with ten players after the red card. We finished the game with two players [born in] 2005, one in 2004.
"Pascal Gross was at right-back, Hinshelwood was at left-back and he's not a left-back. [Joel] Veltman was at centre-back. [Jakub] Moder didn't play in the last two years."
Brighton's victory has helped them climb to seventh in the Premier League table, one point behind Newcastle United in sixth and four points adrift of Tottenham Hotspur in fourth, who face fifth-placed Aston Villa in North London on Sunday.
The Seagulls now shift their focus to next Thursday's Europa League trip to Greece to face AEK Athens, before returning to Premier League action three days later against Chelsea at Stamford Bridge.