It took Switzerland just five minutes to take the lead in Lens when Xherdan Shaqiri's corner was met by Fabian Schar, who got ahead of Albania goalkeeper Etrit Berisha to head into the net from six yards.
Switzerland should have doubled their advantage when Haris Seferovic fired straight at the goalkeeper from the edge of the penalty are before Albania almost equalised through Armando Sadiku, who hit his effort straight at Yann Sommer after being playing in on goal by Elseid Hysaj.
With eight minutes of the first half remaining, Albania were reduced to 10 men when Lorik Cana received a second yellow card for a deliberate handball on the edge of the penalty area and from the resulting set piece, Blerim Dzemaili struck the woodwork.
Moments later, Dzemaili went close again when curling the ball just past the post from Stephan Lichtsteiner's cutback, while Seferovic forced a good save out of Berisha from the left side of the box.
After a quiet start to the second half, Seferovic saw a well-struck effort kept out by Berisha, while Granit Xhaka tried to get in on the act with a 25-yard strike that cleared the crossbar.
Highly-regarded Breel Embolo was introduced on the hour mark and almost provided an assist for Seferovic but after the striker burst clear of the defence, Berisha stayed big to block his effort.
With 15 minutes remaining, Embolo curled over from a promising position and he was almost made to pay when Sadiku was provided with the chance to equalise for Albania from close range, only to see his near post effort hit the side-netting.
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Albania should have been awarded a penalty with 10 minutes to go after Ermir Lenjani was hauled down by Schar but the referee waved the appeals away, and they should have found an equaliser soon afterwards when Shkelzen Gashi beat the offside trap before seeing Sommer pull off a remarkable save from 14 yards out.
Albania tried to force another late chance but they ran out of steam as Switzerland moved level on points with France at the top of Group A.