Gary Speed must wish that qualification for Euro 2012 was just starting rather than coming to a close. After spending so much time propping up Group G, Wales have belatedly found some form, following up their victory over Montenegro last month and a spirited display at Wembley with an accomplished performance here against a Switzerland side whose hopes of reaching the finals next year were extinguished.

Reto Ziegler's harsh dismissal for a clumsy but hardly malicious challenge on Chris Gunter, 10 minutes into the second half, paved the way for Wales to pick up their second competitive win under Speed. The Wales manager looked on with satisfaction as Aaron Ramsey converted from the spot, after Timm Klose brought down Gunter, to give Wales a deserved lead that the outstanding Gareth Bale extended when he ran clear in the 71st minute before stroking the ball home with the minimum of fuss.

Bale was a constant threat with his penetration and pace on the right flank, the Tottenham Hotspur winger unplayable at times as he tormented the Switzerland defence. He was not alone in catching the eye on a night when Joe Allen, who was one of three Swansea City players in the Wales starting line-up, marked his first full cap with a polished midfield performance that was in keeping with the outstanding form he has been showing at club level. A promising international career lies ahead on this evidence.

It was, however, a sobering evening for Ottmar Hitzfeld and his Switzerland players, who left the field believing that they still had a chance of appearing in Poland and Ukraine next summer, only to learn moments later that Montenegro had scored a late equaliser against England to guarantee second spot. Wales, remarkably, could still finish third if they defeat Bulgaria in Sofia on Tuesday and Montenegro win in Basel against a Switzerland side whose morale must be on the floor after this chastening defeat.

Although Ziegler was highly unfortunate to be given a straight red card by Bjorn Kuipers, the Dutch referee – Speed admitted the decision was "harsh" and made a point of consoling the former Tottenham Hotspur full-back as he left the field – it was difficult to have too much sympathy with a Switzerland side that played within themselves for long periods. Wales had looked the more likely to score before Ziegler departed and should have had a penalty moments earlier when Valon Behrami, the erstwhile West Ham United midfielder, brought Bale down in the penalty area.

If the home supporters were upset with Kuipers's decision to wave play on, their mood was soon to change. Ziegler was sent off three minutes later and with Switzerland still reeling from that setback, Klose brought down Gunter after the Nottingham Forest defender ran on to Allen's angled pass. Ramsey's kick was struck low and true and from then on there looked to be no way back for Switzerland.

That much was confirmed when Bale ran clear, after being released by the selfless Steve Morison, and passed the ball beyond Diego Benaglio and into the corner of the net.

"I think with the players we've got we have the potential to do something special but everything's got to fall into place," said Speed, whose mind has already turned to qualification for the 2014 World Cup in Brazil.

"We have to keep working and improving on tonight's performance, although I don't think Gareth can improve that much – he's a sight to behold in full flight. I also thought Joe was excellent – he's playing great for Swansea and he showed he can play at the top level."