Former Liverpool striker Mark Gonzalez came off the bench to head Chile to within touching distance of the last 16.
The 25-year-old, now at CSKA Moscow, struck with 15 minutes remaining as Switzerland, reduced to 10 men when Valon Behrami was sent off before the break, finally succumbed at the Nelson Mandela Bay Stadium in Port Elizabeth.
His goal will send the South Americans into their final Group H clash with Spain knowing a point will be enough to take them through to the knockout stages.
Switzerland, looking to build upon their shock victory over the Spaniards, found themselves up against it even before their numbers were reduced.
Goalkeeper Diego Benaglio had to make a fine double save from Arturo Vidal and Carlos Carmona with just 10 minutes gone, and he was in the right place at the right time five minutes before the break when Alexis Sanchez toe-poked a shot towards goal with his defenders once again conspicuous by their absence.
In the meantime their task had increased markedly when Behrami, having tangled with Jean Beausejour, did so with Vidal and saw the midfielder go to ground clutching his face.
Referee Khalil Al Ghamdi had little hesitation in producing a red card and the Swiss were very much on the back foot.
In truth, they had been already for much of the first half with Chile's midfield trio of Vidal, Carmona - who will miss the final group game against Spain after picking up a second booking - and Matias Fernandez repeatedly causing problems.
Switzerland offered little in response and skipper Alex Frei, who missed the opening game through injury, departed before the break having struggled to make an impact.
Sanchez in particular made a nuisance of himself as the South Americans stepped up a gear in the wake of Behrami's exit, although the Swiss just about held firm.
Chile thought they had taken the lead within three minutes of the restart when Sanchez blasted home a shot with the help of a significant deflection, but an offside flag correctly halted his celebrations in their infancy.
Benaglio needed to be at his best once again with 55 minutes gone when defender Stephane Grichting gifted the ball to Sanchez, who raced in on goal but could not beat the goalkeeper one-on-one.
Half-time substitute Gonzalez headed over from a Fernandez corner but, as the game became increasingly bad-tempered, Fernandez, who will also miss the Spain game, Gokhan Inler and Gary Medel were all cautioned in quick succession.
Grichting made a fine 69th-minute block to deny substitute Esteban Paredes, but it was he who did the damage with 15 minutes remaining when he rounded Benaglio and crossed for Gonzalez to power a downward header in off the underside of the bar.
The lively Paredes might have doubled his side's advantage twice within the final six minutes but was unable to hit the target on either occasion, and Swiss substitute Eren Derdiyok passed up a glorious opportunity to level with seconds remaining when he fired wide.