The game proved a tough test - made all the more difficult due to Eden Hazard's absence through injury - but Cahill, who had earlier given away a penalty, secure a 2-1 victory at a venue where a loss last season had seen the Blues slip to 16th.
Willian had given them the lead with a free-kick only for the Potters to draw level through Jonathan Walters' penalty in a fiery contest that featured Diego Costa as its chief antagonist, though it was Phil Bardsley who saw red in stoppage time.
Simon Johnson was in attendance at the bet365 Stadium to take in all the key talking points...
Chelsea will enjoy this result, but won't look forward to playing Stoke again
One look at Chelsea's record at Stoke City beforehand would have been enough to suggest they were facing a difficult afternoon.
On their previous six visits in the league, they have won just twice and they were also knocked out of the League Cup here last term.
Stoke tend to raise their game against the Blues, as we saw at Stamford Bridge earlier this season when they equalised twice before Antonio Conte's men went on to win 4-2.
The home supporters are renowned for creating a hostile atmosphere, particularly when the big boys are in town and Chelsea looked rattled from start to finish.
Still, they had the last laugh and now they boast a remarkable 13-point lead ahead of Tottenham and Manchester City's games on Sunday.
Marcus Alonso's pace lets him down
Chelsea are looking at strengthening in the wing back position this summer and Alonso has reason to be worried.
He has performed better than many expected and has weighed in with four crucial League goals.
But the Spain international still doesn't make the most of the time and space he gets on the pitch.
There were several occasions that he was found in a great attacking position, but his lack of speed meant he was easily caught up by the Stoke defenders.
A faster man would have got a cross or a shot in and it was noticeable how he was sluggish when defending at the other end too.
There is nothing wrong with the former Real Madrid trainee's technique, as he showed with a fine free-kick that hit the bar.
Alonso will clearly still be in the squad next term, but his first team place may not be guaranteed.
Gary Cahill makes amends for a moment of madness
Cahill has been given the responsibility of wearing the captain's armband now that John Terry is no longer a first-team regular.
For the most part, he has handled the accolade with aplomb but he had some explaining to do this afternoon.
Granted the decision by referee Anthony Taylor to award a penalty in the first half for a push on Jonathan Walters was a soft one.
But Cahill shouldn't have given Taylor a choice to make in the first place. Erik Pieters free-kick was drifting harmlessly into the hands of Thibaut Courtois.
It gifted Stoke, who barely caused an attacking threat all day, an easy opportunity to equalise and Walters took full advantage.
Being the leader of the side means you have to also lead by example and Cahill didn't dwell on his mistake.
Not only did the England international carry on the fight under a barrage of crosses from Stoke, he scored the crucial winner that gave Chelsea a priceless win.
Chelsea will have to get used to being kicked from now on
Manchester United spent the FA Cup quarter-final trying to unsettle Chelsea from their rhythm with constant fouls.
It might have worked too, had Ander Herrera not been foolish to earn a second yellow card.
Stoke were clearly watching as they played with similar aggressive intent and again Chelsea struggled to deal with it.
Hazard was the main target by United earlier in the week, this time it was striker Diego Costa.
Unlike the Belgian, Costa has a short fuse and looked like a red card waiting to happen for much of the match.
By making him angry, Stoke distracted him from what he's good at and he was more focussed on settling scores than adding to one.
Other players were on the receiving end too and surely other teams will employ the dark arts from now on against them.
Hazard still can't come back soon enough
Chelsea fans feared the worst when news emerged that the attacking midfielder was ruled out with a leg muscle injury.
Hazard has returned back to his best this season and has proved the difference on many occasion.
All 11 of his goals have come in the league, but his mere presence on the pitch sparks fear in the opposition.
The Chelsea players exude a lot more confidence in possession too. Even when Hazard is below par, there are more gaps for the others to exploit because teams commit so many defenders to mark him.
The injury is minor and with a two-week international break coming up, he has plenty of time to get fit.
Chelsea certainly missed his creativity this afternoon, with Willian and Pedro not having that bit of magic in open play to cause a threat.