Brazilian winger Kenedy tapped home to make it 1-0 at Stamford Bridge.
Forest were overpowered, Belgium striker Batshuayi doubling the lead before Charly Musonda made it 3-0.
Batshuayi added a fourth before completing his hat-trick on 86 minutes, Tendayi Darikwa scoring a late consolation for Forest.
Chelsea could even afford the luxury of giving former Exeter City defender Ethan Ampadu, who has only just turned 17, his debut in the 55th minute.
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