Chelsea captain John Terry opened the scoring with a fine header before being stretchered off after a nasty collision with Suarez.
The Blues are now without a win in three games, dropping to third place with 24 points and are below title rivals Manchester United and Manchester City.
Elsewhere, Edin Dzeko scored the winner two minutes from time for champions City against Tottenham Hotspur at the Etihad. The Citizens fought back to win 2-1 after Sergio Aguero cancelled out Steven Caulker's opening goal.
Roberto Mancini's side are now second below rivals United with 25 points while Dzeko is City's top-scorer this season with 6 goals.
Newcastle United were stunned by former captain Kevin Nolan after scoring the only to hand West Ham United vital three points away at St James Park.
The Hammers climbed their way up to sixth place with 18 points while Newcastle are currently 10th with 14 points.