Earlier, Cahill had been penalised for a foul on Jonathan Walters, which allowed the Stoke man to cancel out Willian's opening goal.
The defender pounced on a poor Erik Pieters clearance at a corner three minutes from time to reward Chelsea for their dominance.
A wayward pass from Pieters gifted Chelsea a free-kick in the closing stages, and when he failed to clear David Luiz's header from the resulting set-piece, Gary Cahill struck an 87th-minute victor.
Antonio Conte refused to accept it was Chelsea's title to lose after they marched 13 points clear at Stoke.
GK Thibaut Courtois, 6 - Had little involvement in the game until facing Jon Walters' penalty.
He stated: "I think Diego is showing to be very disciplined and showed me great commitment for the team and not himself and I want this from my players".
Shorn of the services of Eden Hazard, Chelsea proved they can function admirably without the gifted playmaker.
A 15-minute cooling off period eased the simmering tension and Chelsea started the second half brighter with Alonso only stopped by a terrific Bardsley challenge and David Luiz's 40-yard free-kick nearly catching Grant out. "He is a type of player who is very hard to stop and for this reason you try to stop him with a good or bad way", Conte said.
"Diego Costa played very well and showed great discipline".
Only once in Premier League history have Stoke beaten the side who are top of the table. The response was a yellow card and Conte sent Michy Batshuayi to warm up as an attempt to remind his striker to focus on testing Grant instead. The only side in Premier League history to have done this in a whole 38-game season were Manchester City in 2014-15 (114/114).
FW Willian, 8 - Handed a rare league start in place of the injured Eden Hazard, Willian served up a typical piece of Samba-style free kick wizardry when tricking the Stoke defence and Grant into thinking he was going to cross the ball instead of firing at the goal.
Pedro blazed over a good chance to restore the visitors' lead before Bardsley clattered into Costa to be booked in the final stages of a tempestuous half.
'We have given a good account against the champions elect'.
13' - GOAL! Stoke 0-1 Chelsea (Willian). Stoke are ninth in the Premier League for a reason and Chelsea departed the bet365 Stadium pitch tired in the knowledge that their 22nd victory of this remarkable campaign was also one of the hardest to earn.
New Lotus Elise Sprint is one of the lightest sports cars ever
Keen maths enthusiasts will point out that adds to 26kg and not 41kg, but every auto in the Elise range is now 10kg lighter. Before this becomes too cynical though, a lighter Elise is surely a better Elise: "Less mass means more Lotus", apparently.