It's fair to say the Barcelona loanee grabbed his chance in emphatic fashion. He opened the scoring, added an assist and played a prominent role throughout.
Let's take a look back at the game's stand-out performance that officially introduced Deulofeu to Premier League audiences.
Everton have been playing in a 4-2-3-1 formation with Gareth Barry and James McCarthy in the deeper berths behind a trio of attacking midfielders.
Deulofeu initially took the right-sided attacking slot, Leon Osman occupied the central area and Steven Pienaar lined up left.
Pienaar was the most fluid of the trio, regularly drifting infields and interchanging with Osman to create overloads that regularly troubled the Potters.
This also brought a lot of the play to Deulofeu and Everton's right. Roberto Martinez has used Mirallas on that flank this season, instructing him to hug the touchline and stretch the field, which is how the Catalan winger started.
Switch to the Left
On the right, Deulofeu hit the byline and crossed; however, with Stoke City's towering defensive line, it soon became clear this wouldn't be an avenue to regular success.
A yellow card to the Potters' right back, Geoff Cameron, provoked a much-needed change from Martinez just before half-time, as he switched Deulofeu to the left in order to run at and expose the American.
As this picture shows, just two of the Catalan's deliveries came from the left, as Deulofeu's responsibilities completely changed once he shifted flank.
On the left, the onus was suddenly on the right-footed Catalan to cut in and pass or shoot, instead of cross, as reflected by the position of most of his shots.
Deulofeu made an immediate impact, scoring having exchanged a number of one-twos on a diagonal run into the box.
He remained on the left into the second half, with Osman filling in on the right and Pienaar moving into the middle, in what became an increasingly fluid system.
The Catalan was heavily involved in the Toffees' second goal, driving forward and attracting markers before squaring to Barry, who found Seamus Coleman to score.
Deulofeu also created Bryan Oviedo's goal and caused more trouble as Stoke were forced to press forward, ghosting past defenders and displaying some mesmerising trickery. It's fair to say this move to the left had a huge bearing on the final outcome.
Martinez enjoys stretching the field and saw Deulofeu return to the right for phases of play, but he was clearly far more effective on the left, terrorising the already booked Cameron.
So we know Deulofeu had a large impact on the game but how did he measure up statistically?
|Shooting||5 shots (4 on target), 1 goal|
|Creativity||2 chances (1 assist)|
His crossing numbers were poor, with just one of 12 finding a man, which highlights Martinez's decision to change his position. It soon became clear crosses were too easily dealt with by Stoke and even corners were rarely delivered into the box.
However, a few over-hit crosses are about all that can be used to mark Deulofeu's card. His dribbling numbers emphasise his explosive potential, including passing two opponents in the Stoke penalty area.
No other Everton player dribbled past as many opponents as Deulofeu and the winger beat more opponents than the Stoke team combined.
He made 68 touches but just 26 passes, highlighting his tendency to cross or shoot. His responsibility was very much end product.
No other player had more crosses or shots than Deulofeu and with the opening three goals heavily influenced by his work, it's fair to say his full debut was a major success.
Everton were especially fluent in this system with Mirallas and Ross Barkley on the bench. Who plays against Manchester United on Wednesday is looking an especially tough call for Martinez.