Switzerland, bidding to reach the knockout stages for the first time, scored in the fifth minute and were given a further boost by a second yellow card for Albania skipper Lorik Cana.
The Swiss took the lead when goalkeeper Etrit Berisha rushed out to clear a corner, but could only lunge at centre back Schaer who rose unchallenged to head in.
Cana’s dismissal for a second yellow card after a handball in the 36th minute seemed to have more or less sealed it for the Swiss, whose keeper Yann Sommer had brilliantly prodded out a shot from striker Armando Sadiku five minutes earlier.
After Cana’s exit, Switzerland besieged the Albania goal, also hitting the post, and could have been two or three up at the break.
The Swiss had several chances in the second half kept out by Berisha, notably in the 66th minute when striker Haris Seferovic was put through with only the keeper to beat.
With 15 minutes to go, Albania’s Italian coach Giovanni De Biasi threw on Sokol Cikalleshi as a second striker and within a minute Sadiku hit the side netting from a narrow angle.
Albania’s golden chance to equalise came three minutes from time when substitute Shkelzen Gashi sprang the Swiss defence and had time and space to think, only for Sommer to expertly parry his over the bar.
It was only the second Euro finals victory for Switzerland and the first one with any meaning as they joined hosts France at the top of Group A.
Swiss Granit and Albania’s Taulant Xhaka became the first brothers to play against each other in a European Championship. The game also featured a host of other players with Albanian roots who could have opted to play for either side.
Albanian fans were initially the most vocal inside the stadium in Lens, periodically booing midfielders Xherdan Shaqiri, Valon Behrami and others they felt should have been playing for them.
Albania, who have now failed to beat Switzerland in seven attempts, will travel to Marseille on Wednesday to face hosts France. Switzerland face Romania the same day.