Taiwo Awoniyi marked his 100th Forest appearance with the early opener at Stamford Bridge and Igor Jesus's penalty doubled their advantage soon afterwards.
The 18-year-old Senegal international put a virtual second-string PSG side ahead after only six minutes with a fortuitous goal in a 2-2 Ligue 1 draw against Lorient.
Top players, including world number ones Jannik Sinner and Aryna Sabalenka, kept up the pressure on the Grand Slam tournaments with a letter to Roland Garros expressing "deep disappointment" over the French major's 2026 prize money.
Manchester United beat Liverpool 3-2 to seal a return to the Champions League next season, while Tottenham climbed out of the Premier League relegation zone with a 2-1 win at Aston Villa on Sunday.
Teenager Kimi Antonelli extended his lead in the drivers' world championship with a historic victory for Mercedes ahead of McLaren world champion Lando Norris in Sunday's dramatic Miami Grand Prix.