A bizarre scuffle between Levi Colwill and James McClean after two minutes could have set an unusual tone for what was effectively a training exercise in front of just over 32,000 fans at the Levi's Stadium.
However, the football soon took centre stage with Christopher Nkunku's instinctive first-half strike being cancelled out by Luke Bolton on 58 minutes before Jack Marriott put the League One outfit into the lead with 19 minutes remaining.
Chelsea would get the draw that their perseverance merited in the closing stages, Lesley Ugochukwu calmly finding the bottom corner from inside the penalty area, to ensure that the Blues avoided defeat in the first of five contests across the pond.
Tensions boil over within 121 seconds
While Chelsea's players were no doubt motivated to impress under Maresca, the Italian probably did not expect one of his international players to become embroiled in a squabble soon after kickoff.
An innocuous-looking challenge from McClean riled Colwill, who proceeded to confront the veteran Irishman in an exchange which required teammates from both sides to calm matters down.
Smartly-taken goals aplenty
Nkunku netted the first goal of the contest with 35 minutes on the clock. A goalbound effort struck Colwill on the back of the leg and fell fortuitously into the path of the French attacker, who lashed the ball into the bottom corner from 10 yards out.
Wrexham's equaliser was well made, a low cross into the box missing everyone, including goalkeeper Lucas Bergstrom who could have done better, and finding Bolton at the back post, who slotted his effort past a sprawling defender and into the corner.
Thirteen minutes later, Marriott found space down the left-hand side of the Blues backline, taking advantage of Chelsea giving the ball away in midfield.
Rather than bide his time, the 29-year-old advanced towards the edge of the area before ruthlessly firing a strike into the far bottom corner of Bergstrom's net.
Ugochukwu's equaliser lacked the power of Marriott's, yet it was equally composed. A neat touch from Armando Broja set up the midfielder to arrow a low shot into the far corner, leaving the goalkeeper unmoved.
A key exercise for Chelsea
Although Maresca would have preferred to start with a victory over lower-league opposition, the positives far outweighed the negatives.
Wesley Fofana and Romeo Lavia each got 45 minutes under their belts after missing all but a few minutes of last season, while new arrival Marc Guiu made a positive impact in attack on the back of his move from Barcelona.
Carney Chukwuemeka notably came through 90 minutes, somewhat of a surprise given his struggles for full fitness last season and the fact that he had never played 90 minutes in a competitive senior game. Perhaps something noted by Maresca during his endless off-the-pitch research.
There were also appearances for potential stars Josh Acheampong and Tyrique George. The two 18-year-olds each showed moments of quality and inexperience, and it will be interesting to see how many minutes they are given in the upcoming fixtures.
Next up for Chelsea is a clash with Celtic on Saturday evening, before they square off against Club America, Manchester City and Real Madrid.