A ruthless hat-trick in the Potteries took Morata’s tally to seven goals in seven games for club and country since completing his £60million switch from Real Madrid to fill the void left by the controversial Costa.
It left the 24-year-old in perfect shape ahead of Wednesday’s trip to Atletico Madrid in the Champions League, where Morata can expect a hostile reception after his long association with their city rivals.
And goalkeeper Courtois admits Morata is already on the way to replacing his close friend Costa, who could be present on Wednesday after sealing a £57m return to Atletico last week but is unable to play until January.
“He is a very good friend of mine. It will be nice to see him,” said Courtois of Costa, who he first met during his own three-year loan stint with Atletico.
“Diego was an under-rated striker here in England. People paid too much attention to him being a little bully on the field rather than looking at his quality.
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“He is one of the nicest, funniest guys I know. He is also a top striker, so I am happy that until New Year we will not have to face him.
“He was always a nice guy in the dressing room and I have known him for six years.
“But we have bought a new striker and he is doing well so we have to move on. As a friend I will miss Diego, and a player, but Alvaro is doing his job so we are happy.
“A striker lives off goals and he has already scored a few important ones.”
Chelsea have a crunch date with Manchester City next Saturday but first comes the trip to Atletico, where Courtois can expect a warm welcome after his popular loan spells, but Morata can prepare for the opposite.
“He will get a different reception to me, I think,” said the Belgian goalkeeper. “Alvaro played a lot of games against Atletico. I think he scored – but not against me! I still think it will be a big game against his old rivals.”
Morata took just 81 seconds to open the scoring on Saturday, darting beyond a makeshift Stoke back three to collect Cesar Azpilicueta’s long ball and beat Jack Butland.
Pedro made it 2-0 on 30 minutes when he pounced on some poor chest control by Darren Fletcher and rocketed a shot past Butland.
And Morata added two more after half-time – a run and shot from a tight angle and a tap-in from Azpilicueta’s chested pass.
It meant a miserable afternoon for Stoke, who began the day with Bruno Martins Indi as their only available centre-back and ended it with even the Dutchman on the sidelines with a groin injury.
Midfielder Joe Allen said: “Injuries or suspensions will have an effect. It seems to be happening to all our centre-halves at the moment. Chelsea is not the ideal team to come up against when you have issues like that.”
STOKE (3-4-3): Butland 6; Johnson 5, Martins Indi 4 (Afellay 77), Pieters 5; Diouf 6, Fletcher 4, Allen 6, Ramadan 6; Shaqiri 7, Jese 5 (Crouch 61, 6), Choupo-Moting 6. Booked: Shaqiri, Crouch. NEXT UP: Southampton (h) Sat, PL.
CHELSEA (3-4-2-1): Courtois 6; Azpilicueta 7, Christensen 6, Rudiger 6; Moses 6, Kante 8, Bakayoko 8, Alonso 7 (Cahill 58, 6); Willian 6 (Hazard 72, 6), Pedro 7 (Fabregas 68, 6); Morata 9. Booked: Alonso, Kante. Goals: Morata 2, 77, 82, Pedro 30. NEXT UP: Atletico Madrid (a) Wed, CL.
Referee: M Dean (Wirral).