But Alvaro Morata scored from close range in the second half from Callum Hudson-Odoi’s low right-wing cross.
The pair later combined again as Morata headed a second at Stamford Bridge.
It was a deserved win for the FA Cup holders, who dominated against a Forest side who are seventh in the Championship.
Hudson-Odoi’s future at Chelsea is also in doubt, with assistant manager Gianfranco Zola saying Bayern Munich are “very interested” in the 18-year-old forward, who won the Under-17 World Cup with England in 2017.
This was only his seventh appearance of the season, and he has yet to start a Premier League game in 2018-19.
With Olivier Giroud, Pedro and Willian missing through injury and Eden Hazard on the bench, Hudson-Odoi got another chance to impress – and he took it.
Playing on the right wing, his excellent deliveries made both goals for Morata, who scored his first goals in six matches.