Forest had a chance to score early on, but Elliot Anderson failed to capitalize on a Chelsea mistake. Instead, he cut inside and was crowded out by Chelsea's defense. A second unforced error by Chelsea handed Forest another opportunity, but Dougas Luiz's header was volleyed over the bar by Morgan Gibbs-White.
Chelsea's attack was lacking, with a weak free-kick from Reece James summing up their first half performance. However, they did create a notable chance, with Andrey Santos' left-footed effort drifting narrowly wide of the target.
At halftime, Chelsea's manager Enzo Maresca made a triple substitution, which breathed new life into the team's attack. The changes paid off, as Chelsea scored their opening goal through Josh Acheampong, who powered home a header from six yards.
Chelsea doubled their advantage just three minutes later, with Pedro Neto scoring a free-kick from the edge of the area. The team continued to dominate, with Igor Jesus turning Callum Hudson-Odoi's cross onto the bar, and then the post, highlighting Forest's struggles.
Chelsea added insult to injury late on, with Reece James scoring a half-cleared corner. A late red card for Malo Gusto soured the win for Chelsea, but not before they had secured a crucial victory.
With Forest's owner Evangelos Marinakis having left his seat early, the writing appears to be on the wall for Postecoglou.