The draw left Chelsea six points adrift of leaders Manchester United, who were also held to a 2-2 at Newcastle on Monday.
Chelsea are still in second place in the Premier League table after having have collected 48 points from 22 games.
Despite their domination, the Blues failed to score a single goal with Didier Drogba and Frank Lampard missing clear cut chances to grab the win.
In the Emirates Stadium, Thierry Henry returned from injury to inspire Arsenal to a 4-0 drubbing of Charlton.
The prolific striker notched a 30th minute penalty-kick home after defender Osei Sankofa brought down Van Persie in the area.
Henry set-up Justin Hoyte with a slick one-two pass just before the break.
Dutch international Van Persie added a second-half brace to hand the Gunners a precious victory that moved up to fourth place on 39 points.