Curiously Stoke were the better side for much of the encounter, but they were ruthlessly punished for defensive lapses as a clinical Chelsea showing fired the champions back up to third in the table.
Morata stole the headlines with his treble, including the opening goal after just 80 seconds, while Pedro also got his name on the scoresheet in the first half as Chelsea returned to winning ways in the Premier League.
Antonio Conte left the likes of Gary Cahill and Eden Hazard on the bench, while Mark Hughes was forced into naming a makeshift defensive line due to Kurt Zouma, Ryan Shawcross, Kevin Wimmer and Geoff Cameron all being sidelined by a mixture of injury and ineligibility.
The stand-in backline was exposed as early as the second minute when Cesar Azpilicueta's long ball forward released Morata clean through on goal, and the Spaniard tucked his finish into the bottom corner for his fourth Premier League goal of the season.
It was a nightmare start to the match for the hosts, but they responded well and looked the most likely to add another for most of the first half.
Stoke failed to trouble Thibaut Courtois despite being the better side, though, and Chelsea punished the hosts' lack of penetration by adding a second on the half-hour mark.
Darren Fletcher's attempted chest back to his defenders only found Pedro, who took a touch before firing a clinical finish into the bottom corner with unerring accuracy.
It was a scoreline which was harsh on Stoke at the interval, but the Potters' clearest chance of the half didn't arrive until the latter stages when Mame Biram Diouf's acrobatic bicycle kick flew wide.
Chelsea's two-goal lead ensured that they had an element of control over the game, but Marcos Alonso threatened that when he almost followed up a first yellow card with a second just two minutes later.
Having seen his side shown three red cards already in the Premier League this season - the same number as they had received in their past 73 league outings - Conte quickly took action to ensure that tally would not grow as Cahill replaced the pantomime villain Alonso.
Stoke continued to probe for a route back into the match, though, and Joe Allen lashed one powerful half-volley over the crossbar from the edge of the area before Xherdan Shaqiri drew the first save from Courtois.
As was the case for the majority of the first half, Stoke were again the better side in the second 45 minutes but could not turn their pressure into goals.
Diouf squandered one difficult half-chance from a tight angle, but Fletcher should have atoned for his earlier error in the final 20 minutes when he lost his marker in the box, only to completely miss his header with only the keeper to beat.
Another free kick from a deep position provided Eric-Maxim Choupo-Moting with a sight of goal moments later, but his header was plucked out of the air by Courtois.
Whereas Stoke were toothless, Chelsea were ruthless and they put the game to bed once and for all with 12 minutes remaining when Morata capitalised on another error to race down the left channel before lifting a clever finish over Jack Butland from a tight angle.
Hazard - on as a sub for Willian - almost added a fourth moments later when his low drive was cleared off the line by Glen Johnson, but it was only a temporary reprieve for the hosts and Morata completed his hat-trick moments later to cap off the scoring.
Having seen three accomplished finishes already it was a fine team goal which added gloss to the result as Cesc Fabregas's chipped pass into the box found Azpilicueta, who chested the ball into the path of Morata allowing his compatriot to apply the simple finish.
It was only after their fourth goal that Chelsea began to look worthy of the one-sided nature of the result, and Morata missed two clear chances to get his fourth of the afternoon when he first fired wide before seeing another effort cleared off the line by Johnson.
Peter Crouch could have seen red for a late challenge on Fabregas in the final minute of normal time, but referee Mike Dean opted for leniency on what was already a frustrating afternoon for the Potters.
The win extends Stoke's wait for a victory to five matches across all competitions, whereas Chelsea are now unbeaten in seven games and have won their opening three away fixtures of a league season for the first time since 2009.
Chelsea face a difficult week ahead, though, with Atletico Madrid to come in the Champions League before taking on free-scoring Manchester City next weekend.