Jose Mourinho said he accepted responsibility for a 5th defeat of the season that leaves Manchester United 11 points adrift of even a top-four finish.
Daniel Sturridge stunned Chelsea with a late goal to rescue a point for Liverpool.
Mohamed Salah got Liverpool up and running as they comfortably dispatched West Ham in their first Premier League fixture of the season.
Shaqiri was one of five recent high profile signings which saw Liverpool shell out more than 200 million pounds in an attempt to close the gap on Premier League champions Manchester City.
The club have spent 174 million pounds ($229 million) on midfielders Naby Keita and Fabinho, winger Xherdan Shaqiri and, perhaps most crucially, Brazil goalkeeper Alisson.
Xhaka and Shaqiri celebrated their goals by making a "double eagle" gesture with their hands to represent the Albanian flag.
The win puts Switzerland in pole position to make it out of a tough Group E.
World Cup 2018, Brazil vs Switzerland Highlights: Brazil were held to a 1-1 draw against Switzerland at the Rostov Arena
Neymar is expected to start when Brazil start their World Cup 2018 campaign against Switzerland on Sunday at the Rostov Arena.
Poland defeated Switzerland in a thrilling penalty shoot-out as they advanced to the quarter-finals of the 2016 Euro Championships
Switzerland will take on Poland in Stade Geoffroy-Guichard at Saint-Etienne in what will be Euro 2016' first Round of 16 match. The winner will take on either Croatia or Portugal in Marseille.
Switzerland demolished Honduras 3-0 to
The 22-year-old tore his right hamstring while on international duty helping Switzerland book their 2014 World Cup place.
The European champions were held to a 1-1 draw at Freiburg after they leaked a late equaliser.
The English Premier League outfit lead 2-1 from last week's semi-final, first leg in Switzerland and need only avoid defeat in west London to be assured of a place in the May 15 final in Amsterdam.
Germany striker Mario Gomez smashed four goals in Bayern Munich's 7-0 rout of FC Basel on Tuesday and insisted his team have big ambitions as they marched into the Champions League's last eight.
Bayern Munich host FC Basel on Tuesday needing to overturn a 1-0 deficit from their Champions League round of 16 first-leg match, while the Swiss side is looking to claim another major scalp.
Lionel Messi outshone Switzerland's hot prospect Xherdan Shaqiri on Wednesday, scoring a hat-trick as Argentina won 3-1 in an international friendly.