Wales’s hopes of reaching the World Cup finals and a first major tournament ended in heartbreak as Switzerland prevailed from this barmy playoff tie, the wily substitute Fabienne Humm flicking in a deft winner as the second half of extra time ticked into stoppage time. A topsy-turvy contest was heading for a penalty shootout after the excellent Ramona Bachmann, who was forced off late on through injury, cancelled out Rhiannon Roberts’s opener. Switzerland missed a second‑half penalty and Bachmann saw a fine strike disallowed in normal time for offside but there would be no final reprieve as Humm struck to floor Wales, whose distraught players left the pitch with sore eyes. Ffion Morgan sat on the turf wiping tears from her eyes and the goalkeeper Laura O’Sullivan headed down the tunnel gnawing at the inside of her cheeks, presumably replaying the moment that ultimately decided this game. Geraldine Reuteler curled a cross into the six-yard box and Humm dashed towards the front post to help the ball past O’Sullivan. “It is incredibly tough to take,” the Wales manager, Gemma Grainger, said. “We know that the margins at this level are fine. I’m proud that we compete at this level and we’re going to continue doing that.” The game descended into attack versus defence as Switzerland attempted to ramp up the pressure but it seemed as though Wales would eke it out until penalties. Bachmann jinked into the box and forced a save from O’Sullivan before Ana-Maria Crnogorcevic, whose 58th‑minute penalty cannoned off a post, headed wide unmarked from a free-kick. The Switzerland substitute Rachel Rinast volleyed wide at the back post on the cusp of half-time in extra time and the Wales left-back Rachel Rowe headed off the line to deny Riola Xhemaili. The defending was so desperate that Xhemaili was shorn of one of her boots. Wales, who required extra time to overcome Bosnia‑Herzegovina on Thursday, eventually wilted. Switzerland put 15 goals past Moldova in their previous game and are nine places above Wales in the Fifa rankings but Grainger’s side had come too far – this was their 12th game of the qualifying campaign – to show any signs of an inferiority complex. Wales seemed to relish their status as underdogs and rocked the hosts when Roberts side-footed in on the turn with 19 minutes on the clock. Kayleigh Green kept Angharad James’s corner alive in the box, towering above two Switzerland defenders to win a header, and Roberts reacted quickest to squeeze a shot into the corner. A slick move brought Switzerland’s equaliser on the verge of half-time, the Arsenal midfielder Lia Wälti’s clever pass breaking the lines after Reuteler shifted the ball infield. Rowe was lured upfield out of position and Noelle Maritz, fresh from picking up Wälti’s perfectly weighed pass, roamed down the right flank and picked out the former Chelsea forward Bachmann, who effortlessly swept a right‑foot shot into the top corner. Wales were suddenly on the back foot and the Switzerland defender Luana Bühler then headed a corner wide before the half-time whistle. The drama increased in the second half when Crnogorcevic adjusted her feet to convert the rebound after her penalty rattled a post, only for the Swedish referee, Tess Olofsson, to rule the goal out because no other player touched the ball before the Barcelona striker stroked home from close range. Crnogorcevic was made to wait a couple of minutes before taking the spot-kick, as the referee calmed squabbling players. The penalty was awarded after the video assistant referee alerted Olofsson to the ball striking Rowe’s hand as the defender got to grips with Eseosa Aigbogun’s cross. O’Sullivan made a smart save a couple of minutes into the second half to keep out Svenja Fölmli ’s effort from the angle as the hosts sought a winner. At the other end Green saw an effort land on the roof of the Swiss net after latching on to Jess Fishlock’s pass. Bachmann thought she had scored a winner on 84 minutes, only for VAR to kill the party. Bachmann rolled Hayley Ladd and lashed a shot into the far corner from the edge of the six‑yard box but moments later placed her hands on her hips awaiting the VAR review, which found the substitute Riola Xhemaili offside in the buildup. Rowe’s heroics cleared off the line to deny Xhemaili but Humm hushed Wales at the last.