Eden Hazard was initially rested and started on the bench, but Chelsea called the superstar into action as they reviewed their tactics due to an injury for Ruben Loftus-Cheek.
Alvaro Morata was the main beneficiary as he twice found the net in the second half, and a slow start by the hosts was soon forgotten.
Callum Hudson-Odoi started for Chelsea, and the teenager was impressive as he assisted both goals.
Chelsea Have No Creativity When Eden Hazard Is Out
The home side were devoid of ideas before Hazard entered the fray just before half-time.
Loftus-Cheek was injured three minutes before the interval, forcing Maurizio Sarri to make a premature change. Hazard was summoned, with Chelsea's forward line struggling against an inferior opponent.
The second half was more favourable for the Premier League side, and home supporters were clearly more relaxed as their side found the opener.
Hazard and Hudson-Odoi quickly clicked, and the prodigious 18-year-old set up Morata for a goal four minutes after the restart.
It was an important moment for both Hudson-Odoi and Morata, with the pair desperate to prove themselves under their latest coach.
Bayern Munich have reportedly been linked with a swoop for the young Englishman, per the Daily Mail's Sami Mokbel, and Morata has persistently lacked authority as the No. 9.
Sarri will continue to play Hazard at the point of the attack in the weeks ahead, but Morata's brace could ease fears about his form.
The Spain international missed a sitter between his two goals, and he appeared dejected as he found the net—failing to celebrate his effort.
Chelsea have to find a player who can support Hazard in the second half of the season, and a new striker appears an essential purchase.
Hudson-Odoi could provide part of the answer, but Sarri will need to convince the youngster his future remains in the capital.
The Blues will not scoop silverware unless they can add firepower, but the holders completed a professional job against a mediocre Forest team.
Chelsea Must Sell Washed-Up Cesc Fabregas In January
Nostalgia was in the air as Fabregas made a rare start at the Bridge, with the 31-year-old reportedly on the brink of a departure from west London.
Fabregas appeared in line for a farewell goal in the first half, but the midfielder missed from the penalty spot after Loftus-Cheek was fouled.
It was a sad moment for the decorated former Gunner, but his run up to the spot and stutter was unconvincing.
Fabregas lacked his usual influence, and he appeared like an individual who needs a fresh challenge after four years at the Bridge.
Hudson-Odoi was excellent, and the Blues should find a place in their starting XI for the attacking prodigy.
The Daily Telegraph's Matt Law said the young winger should bide his time with his current club before the game:
Matt Law @Matt_Law_DT
Hudson-Odoi is 18 and has made 5 competitive appearances for Chelsea this season. Oliver Skipp is 18 and has made 6 competitive appearances for Tottenham this season. I'd say they are both getting good opportunities for their age right now. No need for Hudson-Odoi to be in a rush
Fabregas' tenure at Chelsea is over, but he has been a formidable talent during his spells in English football.