Leicester dominated possession and created the best chances in the first-half, with Thibaut Courtois making a brilliant stop to deny Wilfred Ndidi, whilst Jamie Vardy, who was looking to extend his excellent goalscoring record against the "top-six" came close on two occasions. Cahill's clearance was eventually completed by a covering Rüdiger, which gave Cahill the opportunity to take a seat and receive some treatment.
Chelsea's misfortunes continued in the second half as they continued to remain on the back foot against their opponents.
Leicester City have won just once in their 11 previous Premier League visits to Stamford Bridge (W1 D3 L7) - winning 2-0 in September 2000, with Muzzy Izzet and Stan Collymore getting on the scoresheet.
However, an under pressure Chelsea side were handed a lifeline when Ben Chilwell received two yellow cards within a space of five minutes to be sent off the pitch in the 68th minute.
The Foxes had the better of the chances and Antonio Conte reacted by replacing Eden Hazard, ineffectual with Leicester's intense closing down robbing him of service, and Cesc Fabregas with Willian and Pedro before the hour mark. "We didn't play well but that's when we need the fans behind us", the 25-year-old told Sky Sports.
"We suffered a lot in the first half".
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The draw has now put Conte's men level with Mourinho's side, who have have a game in hand, which is terrible considering that there was a point in late December when they were favorites for the second spot after dismal showings by the Red Devils.
In the 58th minute, with the scores level at 0-0, Conte strangely chose to replace Eden Hazard and Cesc Fabregas.
Chelsea were camped on the edge of the Leicester box for long periods late on, trying to prise apart the disciplined 10 men in front of them.
After the match, the 48-year-old said his players were exhausted after Wednesday's 0-0 draw with Arsenal in the Carabao Cup.
Somehow Conte must find time to rest and reinvigorate his squad - before draws turn to defeats.