The pressure was on Forest boss Ange Postecoglou, who knew that failure to beat Chelsea would increase his chances of the sack.
His side looked assured in the opening stages, and an unforced Chelsea error handed them a golden opportunity to take the lead through Elliot Anderson.
However, instead of pulling the trigger, he elected to cut inside and was crowded out by white shirts. It was another defensive mishap which handed Forest their next opening midway through the first half.
The Chelsea defence misjudged the bounce of the ball, allowing Douglas Luiz to head back across goal for the unmarked Morgan Gibbs-White, who acrobatically volleyed over the bar from close range.
A Blues side missing the likes of Cole Palmer, Moises Caicedo, and Enzo Fernandez looked toothless in attack, with a tame Reece James free-kick from 30 yards summing up their first-half performance.
Yet, despite their distinct lack of attacking threat in the opening 45 minutes, they did create arguably the biggest chance of the half.
A frustrated Joao Pedro dropped in deep and clipped a glorious ball over the top for Andrey Santos, but the Brazilian’s left-footed effort drifted narrowly wide of the target.
Blues boss Enzo Maresca, who was absent from the touchline after being shown a red card against Liverpool before the international break, had seen enough at half-time and made a triple substitution.
Although none of his changes were directly involved, his changes breathed new life into the Chelsea attack, which yielded the opening goal.
Pedro Neto did the heavy lifting in the build-up, charging down the left before planting a perfect cross onto the head of Josh Acheampong, who made no mistake in powering home from six yards.
Chelsea looked like a different team initially after the restart, and they doubled their advantage just three minutes later when Pedro Neto hammered home a free-kick from the edge of the area.
Igor Jesus turning Callum Hudson-Odoi’s cross onto the bar, and then subsequently the post, was somewhat indicative of the struggles Forest are facing at present.
Chelsea added insult to injury late on when Reece James hammered home a half-cleared corner and added the icing on the cake to what was just their fourth victory from their last 15 top-flight away games, although a late red card for Malo Gusto soured things a little.
With Forest owner Evangelos Marinakis having left his seat long since, it looks like the writing is on the wall for Postecoglou.
Flashscore Man of the Match: Pedro Neto (Chelsea)