Pedro Neto scored both second-half goals as Chelsea inflicted Everton’s first defeat of the Premier League season in a 2-0 win on Merseyside after Morgan Rogers escaped a sending off before the interval.
Chelsea, who managed to keep their first clean sheet in the league for nine months, produced a dominant second-half performance which saw Neto open the scoring 43 seconds after the restart before doubling their lead in the 90th minute.
The victory was marred by a serious-looking head injury to Chelsea goalkeeper Emi Martinez, who was taken to hospital for precautionary tests after being stretchered off in the second half following a nasty collision with Everton's Jarrad Branthwaite in the box.
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Chelsea were fortunate not to be down to 10 men at the break after Rogers was spared punishment following a challenge with Everton's James Garner where his studs were high and he was nowhere near the ball.
"I think it's a minimum yellow, but I called red straight away," former Premier League referee Mike Dean said on Soccer Saturday. "He catches him with his studs just on the inside of Garner's knee, and I think it's a straight red, I really do. It's not a good tackle."
Referee Paul Tierney had produced five yellow cards up to that point in a feisty first half, the first time that had happened since February in the Premier League.
Everton had arguably the best chance of the first half but striker Thierno Barry headed straight into the arms of Martinez, who later produced a fine stop to keep out his former Aston Villa team-mate Jack Grealish's volley.
However, their second-half performance dipped significantly as they managed just a single shot on target after the restart, ending the match with six shots in total, their lowest in a league game since last December.
Chelsea struck the bar late in the first half through the volley of Moises Caicedo - deputising as captain for the injured Reece James - at a corner, before defender Maxence Lacroix had his header cleared off the line in first-half stoppage-time.
The victory, which is Chelsea's first at Everton since August 2022, pushes Alonso's side above their opponents in the table as they move on to 13 points from their first seven games and into the Champions League places for now.
Key moments on Merseyside
27: BARRY SPURNS BIG CHANCE! The Everton striker heads straight into Martinez's arms after being found free in the six-yard box by Grealish's delivery
29: FINE SAVE! Chelsea 'keeper Martinez tips over Grealish's volleyed effort, which he smashed into the ground, to keep the scores level
34: YELLOW CARDS! Everton captain Tarkowski is booked for barging Caicedo off the ball and Rogers joins him in the book as the pair clash in the aftermath.
40: OFF THE BAR! Chelsea strike the bar through Caicedo's volleyed effort after a rehearsed corner routine.
42: ROGERS AVOIDS RED! Already booked, the Chelsea forward is spared punishment after a full-throated 50-50 challenge with Garner despite his studs appearing to catch his opponent's knee.
45+3: OFF THE LINE! Armstrong prevents Chelsea from taking the lead through Lacroix's header at a corner in the final act of the half.
46: CHELSEA SCORE! Neto squeezes the ball past Pickford, who should do better, after being found by Hato in the box from the byline.
66: NASTY COLLISSION! Martinez comes off worse than Branthwaite in a battle for the ball from a cross into the box with the Chelsea goalkeeper staying down.
74: After nearly nine minutes of treatment, Martinez is stretchered off and replaced by 21-year-old Penders, who becomes Chelsea's youngest-ever Premier League goalkeeper.
90: CHELSEA SCORE AGAIN! Neto fires in after picking up the loose ball from Henderson's free-kick to score twice in a Premier League game for the first time and wrap up the win.
Moyes questions why Rogers challenge overlooked
Everton boss David Moyes to TNT Sports:
"[The performance was] not as good as we'd have wanted. We hung in a little bit. We got a bit unlucky with the goals, one came right after half time and was a blow to us. The other one takes a few deflections before it falls to Neto.
"There were parts of the game where we did OK, but mainly we didn't offer enough or create enough.
"I can't think of many chances we had, which is the biggest indictment I can give of our performance. Thierno Barry had a really good chance in the first half but after that I couldn't think of too many."
On the feisty nature of the game: "Harrison [Armstrong] had a great tackle on the far side, [for which he was booked] and I thought it was probably the best part of the first half. People who watch football appreciate it.
"Big part of our game, and I didn't think it was in anyway a free-kick. Their player jumped up and got on with it.
"The Morgan Rogers one on Jimmy [Garner] could have been questioned. We're not saying that we want everything to be a free-kick or stopped. I didn't think the Harrison tackle was refereed correctly."
Alonso hails Chelsea's 'mature' performance
Chelsea manager Xabi Alonso to TNT Sports:
"Very happy with the result and the performance. We needed one of these away wins where we have played very professional and serious, looking solid.
"We looked in control of the game. There were moments for sure when we had to defend but overall the team looked mature, knowing what to do in each moment, knowing we would have a moment.
"That came in the second half and after that we were good with the ball, creating chances, conceding not much. To win away is always tough and we finally got the clean sheet.
"We need to keep working. It is just one game. If it is just one clean sheet, it will be very poor. We need many more. For sure, the first one of the season feels good. We need to keep going, working and being serious."