The Swiss, who finished level on four points with Wales but behind on goal difference, will hope to secure a spot in the knockouts as one of the four best third-placed finishers from the six groups.
Their industrious performance and Shaqiri's finishing bodes well for the next phase if they make it.
"I think we played like a unit, and it was crucial today against this team. We knew if we play good we're going to create a lot of chances against this team, and we did so," Shaqiri told BEIN Sports.
Switzerland coach Vladimir Petkovic is confident his side have done enough to reach the last 16.
"We scored a few goals but unfortunately we had more chances we didn't convert," Petkovic said. "It wasn't a perfect game but it was a good game.
"It should be enough to reach the knockout round."
Turkey, who finished fourth with three defeats, were tipped pre-tournament as dark horses, but will head home after a dismal effort in the group stage.
"When the expectations are high, the disappointment is bigger ... I apologise to our nation. I trust my friends, we have learned a lot from this experience," defender Merih Demiral told Turkish TV.
The game encapsulated Turkey's tournament, as they began full of fire and fury and started at a scintillating pace, only to collapse quickly as Switzerland outmanoeuvred them tactically to take an early lead.
Exasperated, Turkey regrouped and tried again, but they went 2-0 when Zuber found Shaqiri in a similar position, and he curled an exquisite shot beyond the despairing dive of Ugurcan Cakir 20 minutes later.
Turkey had their chances, but Swiss keeper Yann Sommer made a string of superb first-half saves as they searched for their first goal of the tournament.
Irfan Kahveci salvaged some pride for the Turks in the 62nd minute with a spectacular strike from distance to reduce the deficit, but their shortcomings were shown up again when Shaqiri fired home to complete a surging counter-attack.
With Shaqiri withdrawn, Granit Xhaka hit a post with a free kick as Switzerland continued to chase the goals that might have enabled them to take second spot, but to no avail.
For Turkey it was a dispiriting end to the as their talent-filled squad proved toothless in attack, in stark contrast to an effective Swiss outfit that may just live to fight another day.
"This young team will mark the next 10 years of Turkish football but we are well aware that such a performance at this tournaments is unacceptable," Turkey manager Senol Gunes said.
The 69-year-old coach, who led Turkey to a stunning third-place finish at the 2002 World Cup, has been back at the helm since 2019.
"I do not think of resignation at the moment, the bill of failure has to be paid but media is also responsible, the management is also responsible, the coaching team is also responsible," Gunes said.