Willian's clever free-kick caught out Stoke goalkeeper Lee Grant to hand the visitors the lead on 13 minutes, before Bruno Martins Indi had an equaliser ruled out for Saido Berahino's off-the-ball push.
Stoke drew level minutes later when Jonathan Walters powered his penalty high into the roof of the net following Cahill's clumsy foul on the Irishman from behind.
Chelsea dominated the second-half, Marcos Alonso hitting the crossbar from a free-kick of his own and Pedro going close, but finally restored their lead in the 88th minute when captain Cahill pounced quickest to a loose ball in the box following a corner.
That ensured that the Blues came away with three points for the 19th time in their last 22 top-flight matches, as they edge closer to the league title.
But Stoke - who were reduced to 10 men in the final minute of stoppage time when Phil Bardsley received a second yellow card - lost at home in the league for the first time since November 19.
Just the one change for either side
Stoke City boss Mark Hughes opted to retain the 4-4-2 formation that was so successful in their credible 0-0 draw at Manchester City 11 days earlier, the only change seeing Marko Arnautović - having recovered from his bout of sinusitis - replace Mame Biram Diouf.
Xherdan Shaqiri remained missing from the match-day 18, despite having been touted for a return from a calf injury that has sidelined the winger since January, while Wilfried Bony and Giannelli Imbula were both also absent altogether.
Chelsea had used the fewest players - 21 - and made the fewest changes to their starting line-up - 24 - of any Premier League team this season coming into this one and unsurprisingly made only one injury-enforced change.
Creator-in-chief Eden Hazard missed out with a minor leg injury picked up in training earlier in the week, with Pedro replacing him out wide.
Former Stoke loanee Victor Moses shook off a calf injury that forced him to limp off in the FA Cup quarter-final victory over Manchester United on Monday night, returning to take up his familiar wing-back role in Chelsea's 3-4-3 set-up, while César Azpilicueta was handed his 150th league appearance for the club.
Willian's sixth of the season puts league leaders in front
On a typically windy afternoon in the Potteries, neither side could claim control for the first 14 minutes. The Stoke supporters roared on their side as they looked to press Chelsea high up the pitch, yet there was very little meaningful action.
The home fans also made their feelings towards Chelsea frontman Diego Costa well known, the Spaniard involved in some early tussles with Bruno Martins Indi.
But Costa - with 17 goals to his name ahead of this weekend - imposed his quality when finding Marcos Alonso out wide on the left with a fine pass to start a counter-attack.
Though the wing-back's lack of pace let him down, he forced a free-kick out of Arnautović which Willian then snuck beyond Grant at his near post with a perfectly-executed effort for his first league goal since netting a brace in the reverse fixture between these two teams on New Year's Eve.
Having taken the lead, the Blues began to exert some of the quality that has made them this season's dominant Premier League team - Moses seeing a shot blocked after Willian's back-heel inside the box concluded a well-worked move.
Stoke, meanwhile, enjoyed good spells of possession but continually saw their attacking moves break down in the final third as they struggled to maintain any pressure.
Chelsea came close to extending their lead on the half-hour mark when - from another free-kick - Willian drove a low ball out to Moses on the edge of the box.
Rather than shoot first time, the Nigerian patiently waited and flicked a pass beyond Stoke's back-line for an on-side Alonso to receive, but Grant stood strong to beat his powerful attempt away.
Walters penalty restores parity after Martins Indi has goal disallowed
The Potters grew into the game nearer the half-time whistle. N'Golo Kanté had to turn Arnautović's low cross behind for a corner, from which the home side put the ball in the back of the net when Martins Indi headed beyond Thibaut Courtois from Geoff Cameron's flick-on.
But referee Anthony Taylor sought advice from the linesman on the near side, who ruled the goal out seemingly for Saido Berahino's push in the back of Azpilicueta - though there was initial confusion over whether it had been given for Berahino being in an offside position for Martins Indi's header.
Yet Stoke eventually drew level on 38 minutes after Cahill pushed Walters to ground inside the area at a free-kick and the forward picked himself up to hammer in his third goal of the campaign and his first from the spot.
That came after Stoke had been outplayed for much of the opening 45 minutes, with just one shot and only 38 per-cent possession.
Chelsea on top in search of second to go back in front
And the Potters were forced to remain alert quickly after the restart, Cameron required to deny Pedro a foray into box before Alonso had a left-footed drive deflected wide following Kanté's through ball.
Stoke 'keeper Grant was also fortunate that David Luiz's dipping 35-yard free-kick didn't bounce more wickedly, initially batting away the Brazilian's speculative effort but needing Cameron to clear the rebound as Costa ran in to meet the loose ball.
Chelsea were undoubtedly the team on top and were close to re-establishing a lead when Alonso curled a free-kick back off the crossbar from 22-yards after Pedro had been crudely brought down by Erik Pieters on the break-away.
Shortly after Nemanja Matić had a low effort well held by Grant, Conte turned to Cesc Fàbregas - having scored seven and assisted twice in eight starts against Stoke - from the bench with 20 minutes remaining.
Stoke retained good defensive shape but Chelsea enjoyed almost all of the possession, and Grant's fingertip save kept out Pedro's venomous strike as the Londoners continued to crank up the pressure.
Cahill strikes late to hand Chelsea another victory
Hughes' charges ventured further forward as the game crept into its final stages, though could only fashion half-chances - none of which they could take.
And Chelsea finally scored a second goal to spark wild celebrations in the away end - and on the touchline as Conte wheeled away jubilantly - when David Luiz met Fàbregas' corner with a header that Pieters couldn't clear, allowing the ball to drop for Cahill who fired high into the top corner to make it 2-1 with three minutes of normal time left.
Conte introduced Kurt Zouma after that, meaning Chelsea have utilised all 84 of their available substitutes so far this season, and they went close to adding further gloss with a third.
Costa struck the post late on before Grant denied the striker with another low stop, but the 'keeper could not prevent Chelsea walking away with another win and taking one step closer to an inevitable league title, as they opened up the gap further on rivals Tottenham Hotspur in second.
Stoke, meanwhile, are still without a win against any of the league's top 12 and remain ninth - though 10th placed Southampton have three games in hand on them and are only three points behind.