Remo Freuler's brilliant goal early in the second half sent the Swiss through to the knockout rounds for the fourth time in five World Cups.
The Swiss were one of seven European teams whose captains were to wear the armband in support of LGBTQ people at the tournament in Qatar, where homosexuality is illegal.
Granit Xhaka's second-half winner secured Arsenal a 1-0 victory over PSV Eindhoven at the Emirates Stadium and a place in the Europa League knockout phase on Thursday
Premier League leaders Arsenal host Norwegian champions Bodo/Glimt in a Europa League Group A clash at the Emirates Stadium in London
Premier League: Goals from Nuno Tavares, Bukayo Saka and Granit Xhaka powered Arsenal to a 3-1 win against Manchester United at the Emirates Stadium.
Mikel Arteta apologised for Arsenal's "unacceptable" performance in a 3-0 defeat at Crystal Palace that dealt a significant blow to their bid to finish in the Premier League's top four
Premier League: Arsenal will be without Swiss midfielder Granit Xhaka for a lengthy period due to a knee injury.
Euro 2020: Switzerland beat France on penalties in the Round of 16 to progress to the quarter-finals.
Premier League: Mason Greenwood stood out for Manchester United with twin strikes in their 3-1 win against Burnley, while Arsenal survived a scare with a 97th minute equaliser versus Fulham.
Arsenal's chances of a top-four finish in the Premier League look forlorn after Granit Xhaka's error gifted Burnley a 1-1 draw on Saturday.