After losing their opening two league phase games, Ajax already knew they would have their work cut out to leave Stamford Bridge with a positive result.
With that in mind, under-pressure boss John Heitinga could certainly have done without an early red card, which was shown in Kenneth Taylor’s direction for a reckless challenge on Facundo Buonanotte.
The hosts took full advantage of the subsequent free-kick to compound Ajax’s miserable start, working the angle to send a deep cross into Wesley Fofana, who headed the ball back across the box for Guiu to guide home his first Champions League goal for Chelsea.
Moisés Caicedo then added a second to stamp Chelsea’s authority on the contest, with his long-range effort taking a wicked deflection to wrong-foot veteran goalkeeper Remko Pasveer.
Ajax’s brightest moment of a disastrous first period arrived in the 33rd minute when Wout Weghorst squeezed a penalty under Filip Jörgensen after Tosin Adarabioyo trod on Raúl Moro’s foot.
However, Weghorst quickly undid his own positive work as he clumsily slid in on Enzo Fernández to gift the Blues the chance to restore their two-goal cushion.
The Chelsea skipper calmly dispatched the resulting spot-kick before Estêvão took over penalty duties in first-half stoppage time to fire home his first UCL goal after drawing the foul from Youri Baas with his trickery.
With the three points effectively secure, Enzo Maresca took the opportunity to make a triple change at the break, introducing Trevoh Chalobah, Andrey Santos and George.
The latter required just three minutes to make an impression on the one-sided contest, pouncing on a loose ball just inside the box to slot a first-time shot past Pasveer with the aid of a deflection.
More history was made on a perfect night for the Premier League side when Reggie Walsh was introduced to become the youngest player to represent Chelsea in the UCL.
Walsh and his teammates cruised through the remainder of the contest to see out a statement win that moves Chelsea up to 11th, while Ajax remain rooted to the bottom of the standings without a point to their name.
Flashscore Man of the Match: Estêvão (Chelsea)