Second half substitute Edison Flores gave Peru a smash and grab 1-0 victory away to goal-shy Colombia as goalkeeper David Ospina's gaffe cost the hosts in Friday's World Cup qualifier.
Peru stun goal-shy Colombia, Venezuelan Rondon's treble sinks Bolivia
Peru's players celebrate after Edison Flores scored a late winner to defeat Colombia in a South American World Cup qualifier
Salomon Rondon scored a hat-trick as rock bottom Venezuela thrashed 10-man Bolivia 4-1.
Peru barely had a shot on goal all match, but five minutes from time Ospina somehow let Flores's fierce effort from a tight angle beat him at his near post as Peru snatched an unlikely victory on the counter attack.
Colombia had dominated throughout but failed to score for the sixth successive match -- a run of more than 550 minutes.
The result propelled Peru into the final of four automatic qualification spots in the single South American table with three matches to play.
Colombia dropped to sixth, three points behind fourth-placed Peru, who did not manage a shot in the first half.
Uruguay are fifth a point behind Peru, after Luis Suarez gave them a 1-0 victory at Paraguay on Thursday.
With Brazil and Argentina already qualified, six teams a vying for the final two automatic berths.
Hosts Colombia paid for the same lack of clinical finishing that had blighted their previous five matches.
Of 28 shots at goal, only two were on target.
Veteran pair Radamel Falcao and James Rodriguez were lively in the opening period as Colombia probed relentlessly.
James had a shot from outside the area deflected narrowly wide with goalkeeper Pedro Gallese beaten.
Gallese then blocked Falcao's close-range prod after the striker was played in by Matheus Uribe before Falcao shinned an attempted volley high and wide.
The once-prolific 35-year-old also headed over from a James corner.
Falcao and James's influence waned in the second period and Colombia rarely threatened with reported Liverpool and Tottenham target Luis Diaz of Porto a peripheral figure on the left wing.
Colombia came closest when Gallese reacted brilliantly to tip over an inadvertent back header from a defender.
Their profligacy came back to haunt them as Christian Cueva sent Flores scampering away down the left to embarrass Ospina, who had been a spectator throughout.
Venezuela's hopes of reaching Qatar were long over before kick-off but Rondon showed there is hope for the future with a clinical display.
His near post header and then low finish into the corner put the hosts in control in Caracas before Bruno Miranda replied with a bullet header to give Bolivia hope at the break.
Darwin Machis robbed goalkeeper Carlos Lampe after a defensive mix up to extend Venezuela's advantage before Leonel Justiniano was shown a straight red card on the hour mark for a stamp.
Rondon completed his hat-rick midway through the second half with an emphatic finish high past Lampe.
On Thursday, Brazil goalkeeper Alisson Becker was sent off twice in the 1-1 draw away to Ecuador but both times was saved by a VAR review.
The Liverpool goalkeeper was first shown a straight red card for catching Enner Valencia with a high boot in the first half before that was downgraded to a yellow.
And in second half stoppage time he was shown a second yellow for clattering Ayrton Preciado before that was overturned on review.
Ecuador goalkeeper Alexander Dominguez was sent off for catching Matheus Cunha in the neck with his studs, while Brazil's Emerson Royal was dismissed for two bookings.
Casemiro gave Brazil a sixth minute lead but Felix Torres equalized 15 minutes from time.
Ecuador, who had two penalty awards also overturned by VAR, stay third with a five-point gap to fifth-placed Uruguay.
Seventh-placed Chile's hopes suffered a blow as they were beaten 2-1 at home by Argentina.