Having been left without a striker through Dominic Calvert-Lewin's knee injury and Salomon Rondon's suspension, Frank Lampard's hosts sat deep and successfully frustrated Chelsea early on.
But Everton's resistance was finally broken when Jorginho converted from the spot on the stroke of half-time, and the Toffees were unable to find a way past Edouard Mendy despite an improved showing after the break.
That meant Chelsea won its Premier League opener for a third consecutive season despite failing to produce a fluid performance on Merseyside.
Everton suffered an early blow when Ben Godfrey was carried off with a serious lower-leg injury, but they forced Mendy into the first meaningful save through James Tarkowski's 24th-minute header.
Chelsea debutant Raheem Sterling was denied by the offside flag 42 minutes in, having stabbed home after Jordan Pickford fumbled N'Golo Kante's effort, but Chelsea made its dominance count nine minutes into a lengthy bout of stoppage-time.
Abdoulaye Doucoure hauled Ben Chilwell down as the wing-back burst into the area, allowing Jorginho to convert neatly into the bottom-left corner as Pickford went the wrong way.
Everton found Mendy in inspired form as they looked to respond after the break, with the Senegal stopper denying both Demarai Gray and Doucoure with strong saves.
Ten minutes of additional time were signalled after a medical emergency in the crowd required a brief stoppage, but Chelsea's experienced rearguard stood firm.