The Spain international was in inspired form against his old club as the Blues secured a narrow victory over their London rivals at Emirates Stadium.
Arsenal had to play most of the game with 10 men after Per Mertesacker was sent off for bringing down Diego Costa, who was through on goal.
Costa then scored the eventual winner in the 23rd minute when he finished from close range.
Fabregas was in good form at The Emirates and was named the man of the match after the game.
And former Liverpool midfielder Redknapp admits that it was a welcome performance from the Spaniard, who has been criticised for his form this season.
Redknapp wrote in his column for the Daily Mail: “This was always going to be a tough game for Cesc Fabregas. He’s been portrayed as someone who badly let down Jose Mourinho and always has a point to prove against Arsenal.
“Fabregas ran the game, and not just after the red card — he was in control from start to finish and completed 70 passes, the joint-best on the pitch.
“That will put some credit in the bank with the Chelsea faithful.”
Chelsea’s next Premier League game is a trip to Watford on Wednesday 3 February.
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