The Blues produced a chaotic defensive performance in a 4-1 humbling by the Scottish champions, making it six goals conceded in three halves of football when including the second 45 minutes versus Wrexham.
However, Enzo Maresca witnessed his team produce a far more polished display at the Mercedes-Benz Stadium in Atlanta, helped by a third-minute penalty from Christopher Nkunku.
Marc Guiu and Noni Madueke, from the spot, also got on the scoresheet as Chelsea showed signs that they are capable of implementing Maresca's strategy faster than many may have anticipated.
This success is made all the more impressive through their opponents having already played four competitive matches in Mexico's top flight since the start of July.
Guiu header sandwiched between penalties
Mauricio Pochettino had to deal with his fair share of penalty issues during his one-year reign, and it appeared that Maresca may have to cope with the same issue in Georgia.
Madueke wanted to take the resulting spot kick after Romeo Lavia's driving run resulted in him being upended in the box, only for Maresca to instruct Tosin Adarabioyo to run over and ensure that Nkunku was given the responsibility.
The situation was diffused almost immediately, Nkunku being passed the ball before drilling his effort down the centre of the goal for his third strike in as many pre-season games.
Chelsea's second at the midway point of the first half was wonderfully crafted. Raheem Sterling's precise pass found the advancing run of Kiernan Dewsbury-Hall - making his first appearance of the US tour - and his first-time cross to the near post was glanced into the net by Guiu.
While there has been talk of the former Barcelona prospect going out on loan, the 18-year-old has done nothing wrong in his first three appearances in a Blues shirt and, as it stands, looks far more likely to remain at Stamford Bridge than leave for a year.
Even with Nkunku still on the pitch, Madueke got the chance to take Chelsea's penalty. It had been won by the Frenchman, who glided past numerous Club America players before being clipped by the goalkeeper.
Madueke showed last season in a Premier League fixture against Crystal Palace that he can be cool from the spot, and the winger replicated that composure here with a deft finish into the top corner.
Other takes from Chelsea win
The biggest surprise was that there were only four alterations from the Celtic game, particularly Lavia and Nkunku retaining their places after their fitness issues from 2023-24.
Even with other players to come back into the squad, the duo have been the shining lights of the US tour thus far and look on course to start against Manchester City on August 18, should they stay fit.
Dewsbury-Hall's first outing in a Chelsea shirt could not have gone much better, the former Leicester star showcasing his greater understanding of the Italian's system than his teammates.
Any transfer speculation involving Madueke can seemingly be ignored, the winger playing at least 79 minutes for the second game in succession, while Wesley Fofana got another 28 minutes in the tank as he continues to search for sharpness after a year out.
Enzo Fernandez, fresh off the back of resolving the racism row with his Chelsea teammates, also played for 45 minutes, perhaps unexpectedly after only featuring in the Copa America final on July 14.
Carney Chukwuemeka was left on the substitutes' bench having featured heavily in the opening two games, and new goalkeeper Filip Jorgensen was provided with his debut in the second half. The Dane will hope for a start against Man City on Saturday night.