But it wasn't a convincing victory for Thomas Tuchel's men, as they saw off Blues legend Frank Lampard's Toffees 1-0 in Merseyside.
After a rip-roaring atmosphere at Goodison Park in the early stages, the atmosphere was muted somewhat as Ben Godfrey was stretchered from the pitch with a serious looking leg injury.
It came after a defensive mix-up between the defender and Pickford, leading to a challenge on Kai Havertz that saw Godfrey's leg buckle underneath him.
With Mason Holgate replacing him, it was Chelsea who pushed forward with Blues debutant Raheem Sterling appealing for a penalty after being hauled down in the area, however the referee waved the claims away.
At the other end, Edouard Mendy was forced into an excellent save to deny James Tarkowski who powered a header towards goal.
It looked like the half-time break was approaching with no goals until N'Golo Kante's shot was parried into the path of Sterling who slotted home, only to see the linesman flagging for offside, much to his dismay.
However, Chelsea were handed a penalty just before the break as Ben Chilwell was brought down by Abdoulaye Doucoure, with Jorginho converting with ease.
It is the first time he has netted past Pickford since the Italian midfielder was denied by England's number one during the Euro 2020 final, a match that was decided by penalty shootout.
Asked if the Euro 2020 penalty was on his mind during the penalty, Jorginho told Sky Sports: "Yes, of course you think about it. You work during the week thinking about what the keeper might do in that moment, so I was thinking a lot and took that decision and this time it was the right decision.
"For me a penalty is 70-75% in the head and psychological and so I thought a lot, trained and thankfully today went well."
Everton pushed forward in the second-half with Mendy pulling off a stunning double stop to deny Doucoure and Holgate from close range.
Substitute Dele Alli had a chance to grab an equaliser but fluffed his lines, before Marc Cucurella was brought on to make his Chelsea debut, replacing Kalidou Koulibaly who appeared to pick up a knock.
Cucurella almost made an immediate impact as he cut the ball back to Sterling who sent his effort narrowly wide of the mark with ten minutes to go.
The final stages were delayed due to a medical emergency in the stands, but thankfully the stoppage was brief with the match getting back underway.
Ten minutes were added as stoppage-time as a result but, in truth, Everton rarely looked like getting back into the match and Thomas Tuchel will be delighted with the positive start to the new season.