A goal from young Villa forward Cameron Archer had ensured a draw in normal time.
Levelling with a header after Timo Werner had put the Blues ahead.
Werner’s goal was his first in 11 games for Chelsea and he should have had a second but dragged a shot wide.
Reece James scored the winning penalty in a shootout
The result extends the reigning European champions’ unbeaten start to the season,
which has also seen them top the Premier League with 13 points from five matches.