The 19-year-old made his full Arsenal debut as one of seven changes from the side that lost 3-1 to Manchester United in the Premier League, with only Gabriel Magalhaes, Gabriel Martinelli, Granit Xhaka and Albert Sambi Lokonga holding their places.
Marquinhos let emotion take over when he drew first blood for the Gunners in the 16th minute, but Mikel Arteta's side were pegged back just before half time through Mirlind Kryeziu's spot kick.
However, Marquinhos capped off a dazzling debut with a fine assist for Eddie Nketiah just after the hour mark, and the striker's header proved decisive at Kybunpark.
Unsurprisingly dominating possession in the earliest exchanges, Arsenal counter-attacked brilliantly in the 16th minute, with Fabio Vieira doing well to beat the press and sending Nketiah charging down the left-hand side.
The England striker's cross took a slight nick off of a Zurich defender before falling kindly for Marquinhos, who finished first time into the top corner before allowing the tears to flow.
In doing so, the former Sao Paulo starlet became the first Arsenal player in 41 years to make their debut in a European game and score, following in the footsteps of Raphael Meade against Panathinaikos in 1981.
For all of their ball possession, Arsenal could not add to their lead during the remainder of the first half, and Zurich were awarded a penalty when Nketiah felled Fidan Aliti inside the area.
Kryzeziu drowned out the noise of the travelling Arsenal fans to send debutant Matt Turner the wrong way, and the players emerged from the dressing rooms after the break to the news that Queen Elizabeth II had died aged 96 - a minute's silence was held before the second half commenced.
Arteta's side upped the ante in the early stages of the second half, with Nketiah seeing a tame effort saved and Takehiro Tomiyasu blazing over before the former went from zero to hero.
Marquinhos was heavily involved once again, as the teenager floated a delightful inswinging cross in from the right-hand side for Nketiah to head home at Yanick Brecher's far post in the 62nd minute.
Nketiah's strike saw him become the fifth Englishman to score in three straight Europa League starts - Harry Kane, Bobby Zamora, Jermain Defoe and James Tavernier had previously achieved the feat.
Arsenal were forced to absorb bountiful Zurich pressure in the final moments, but Arteta's side held on to record their first three points of the continental campaign.
In the other game in Group A, PSV Eindhoven and Bodo/Glimt played out a 1-1 draw at the Philips Stadion, and Arsenal welcome the Eredivisie side to the Emirates for matchday two next Thursday.