The conditions made it difficult for both teams, but they each had chances to win the game. Jackson was also denied from point-blank range by Everton goalkeeper Jordan Pickford as Everton kept a fifth clean sheet in six games.
Chelsea keeper Robert Sanchez denied Jack Harrison at the other end with a superb stop, while Iliman Ndiaye's goal-bound shot was blocked by visiting defender Tosin Adarabioyo.
Chelsea remain in second place with 35 points, one behind leaders Liverpool but having now played two games more. Everton climb to 15th with 16 points from 16 games, four clear of the relegation zone.
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