Just as importantly as our clinical finishing, Chelsea managed to finish with 11 players on the pitch.
The former Real Madrid man would complete his hat-trick soon after, via a fantastic team move, to make it six goals in his first six league games for Chelsea. Chelsea boss Antonio Conte: "I think Alvaro played very well and he took his goals very well, which for a striker is very important".
"I am pleased for Alvaro's performance, pleased for the performance of the team".
Tottenham and Watford also maintained flawless away records.
The Belgian missed the start of the season with an ankle injury sustained on worldwide duty at the beginning of the summer, but made his first league appearance as a second-half substitute against Arsenal last week, and was immediately Chelsea's most unsafe player.
Morata's second was even better as he picked up the ball on the left, drove past two Stoke defenders, and curled the shot into the far corner from a tight angle in the 77th. The Blues went home with three points, and the ideal momentum and form for their next two games against Atletico Madrid and Manchester City.
Chelsea remain three points behind leaders Manchester City, who they play at Stamford Bridge in what could be one of the season's formative games next Saturday. Perhaps more worryingly, the Potters fell to a shock 2-0 loss to Bristol City in their Carabao Cup third round match. The Spain worldwide oozed class throughout the game and doubled his tally with another fine individual goal before tapping in his third.
Chelsea are certainly going to score plenty this season with the Spanish quartet linking up with each other.
However, Liverpool's fragile defence was once more exposed as Shinji Okazaki pulled a goal back. Sergio Aguero netted a hat-trick in City's last League match against Watford and another hat-trick against Palace will place him as Manchester City's all-time highest goalscorer ahead of Eric Brooks with 177 goals from 493 appearances. Vardy then squandered a chance to secure the Foxes a draw when his penalty was saved by Simon Mignolet.
However, Pedro Rodriguez extended the lead to 2-0 for the Blues in the 30th minute with a right footed strike from outside the box. "In this stadium the crowd push a lot and I want to thank our fans because I repeat they helped a lot the team today".