An early goal from Fabian Schär proved to be the difference, but he had Yann Sommer to thank for several superb saves.
Lorik Cana also seen red in the first half, but it was still an encouraging performance from the debutants.
Lightning start from the Swiss
It was a lively beginning to the game in Lens, with plenty happening in the opening exchanges. There was early promise for the Swiss after Xherdan Shaqiri fed Admir Mehmedi, only to see his cross cut out by Mergim Mavraj. Granit Xhaka also made his presence felt early on, going in hard to win the ball from Amir Abrashi.
That early tempo and pace paid dividends, as Vladimir Petkovic's side took the lead within five minutes. Shaqiri's corner was inch-perfect for Schär, who rose highest to head home past the stranded Etrit Berisha. The 'keeper had come to collect the set-piece but failed to get anywhere near the ball, ultimately costing his side dear.
Albania battle back
Albania did settle but found it hard to force a way through the Swiss back-line. Despite a few nervous moments, and a yellow card for Schär, both he and Johan Djourou looked comfortable at the heart of the defence. Instead it was Haris Seferovic who went close, but he couldn't convert after stylish play from Blerim Dzemaili.
For some reason, Switzerland seemed to switch off after that and the tides turned in Albania's favour. Some neat play by Odise Roshi saw Taulant Xhaka fire narrowly over the bar from inside the area. An even better chance fell to Aramndo Sadiku after Elseid Hysaj's superb through ball. Yann Sommer brilliantly denied him with his leg, though.
Cana sees red
The other major incident in the half saw Cana recieve a second booking late on in the opening period. The defender slipped and failed to regain his composure when dealing with a through ball, only succeeding in flapping the ball away with his hands; Carlos Velasco Carballo had no choice but to produce a second yellow card.
Dzemaili took the resulting free-kick, right on the edge of the area, and rifled his effort off the post with Berisha beaten. The midfielder came close again as Stephan Lichtsteiner drove forward, though his shot went narrowly off target. Seferovic had one last shot on goal before the break, brining a good save from Berisha in the process.
Berisha keeps Albania in the game
The second half began in slower, more calculated fashion. Sommer was quick off his line to mop up from some dodgy Djourou defending, while Granit Xhaka worked the ball well into Seferovic to shoot hard at Berisha's near post. The 'keeper, however, was equal to the task and produced a fine save.
Breel Embolo came off the bench to have an immediate affect on the game, playing Seferovic through on goal - once more - with a superb through ball. It was more a case of Berisha being pitted against the Eintracht Frankfurt forward, and the goalkeeper came out on top once again with a stellar stop.
Swiss squeeze out three important points
The best late shooting opportunities fell for Albania, and they would have felt hugely disappointed not to take at least one of them. Hysaj's lovely reverse pass pass put Sadiku through on goal but he fired into the side-netting. The best chance of the match fell in the final minutes and to Shkelzen Gashi. He looked certain to score, but Sommer's stunning save ensured Switzerland head into the crucial game against Romania with three points. Albania face hosts, France next.