Two-time World Cup winners Argentina -- who had taken just two points from their first three matches -- claimed their first win, downing Colombia 1-0 in Barranquilla thanks to a first half goal from Lucas Biglia.
Brazil meanwhile produced their best performance of the qualifying campaign to date with a 3-0 defeat of Peru in Salvador.
Bayern Munich star Douglas Costa scored one goal and created two others as Brazil swept aside the challenge of the Copa America semi-finalists.
The victory pushed Uruguay up to second place in the standings with nine points from four games, three points adrift of surprise early pacesetters Ecuador, who made it four wins out of four on Tuesday with a 3-1 win over Venezuela.
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Brazil's victory over Peru left them in third place with seven points, ahead of Paraguay and Chile on goal difference.
Argentina's win in Colombia lifted them to sixth, just outside the top five qualifying spots.
But the Argentinians will feel confident that they can mount a charge back up the table when qualifiers resume in March, when injured stars Lionel Messi, Sergio Aguero and Carlos Tevez should all be fit and available once more.
"We deserved to win, it is fair. We could have scored another goal," said Martino, who said his happiness was more for his players than for himself.
Five-time champions Brazil had a virtuoso performance from Costa to thank for their win.
The Bayern star opened the scoring with a tap-in on 22 minutes from Willian's low cross and then turned provider with a jinking run and pass for Renato Augusto for Brazil's second on 57 minutes.
On that occasion Cavani was sent off after lashing out at Jara when the Chilean defender attempted to poke a finger into the Uruguayan striker's backside.
Jara was later banned for three matches over the incident.
The lingering tension from that encounter was evident in an ill-tempered game at the Centenario and threatened to boil over around the 20-minute mark.
Amid jawing and gesturing between the teams Uruguay were awarded a free kick and captain Diego Godin slotted home the opener from the set-piece in the 23rd minute.
To compound Chile's misery, midfielder Jorge Valdivia was shown a red card after the final whistle, apparently for remarks to referee Wilmar Roldan of Colombia, who also issued seven yellow cards.
Ecuador meanwhile lead the standings after extending their 100 percent record against Venezuela in Puerto Ordaz -- Venezuela's fourth defeat in as many games.
Goals from Fidel Martinez, Jefferson Montero and Felipe Caicedo lifted Ecuador, who exploited a porous Venezuelan defence.