The result left the Argentines, twice former winners, in danger of being eliminated at the group stage.
The first half saw an astonishing quadruple miss by River while the Uruguayans wasted a flurry of chances near the end.
In the 23rd minute, River striker Radamel Falcao Garcia had a shot saved by Rodrigo Munoz, Cristian Fabbiani headed against the bar, Diego Barrado's shot was saved by Munoz and Falcao had another effort cleared off the line.
Marcelo Gallardo hit the crossbar as River pressed after halftime but the closing stages belonged to Nacional.
Nicolas Lodeiro chipped over the crossbar with only goalkeeper Mariano Barbosa to beat and then hit the post before Federico Dominguez and Sergio Blanco both had shots saved.
Fabbiani had raised the temperature for the match by dismissing Nacional's 3-0 win earlier in the group as a fluke.
"They're not good enough to play in the Libertadores and we'll steamroller them," he said, angering the Uruguayan side.
Fabbiani sheepishly shook hands with some of the Nacional players at the end of Tuesday's game.
Nacional lead Group Three with 10 points from four games while River are third with four.
Peruvian champions Deportivo San Martin stayed second with seven points after drawing 1-1 in Paraguay with another team called Nacional.
Striker Martin Arzuaga gave San Martin the lead before halftime and Fabio Escobar headed Nacional's equaliser in the 65th minute.
Brazil's Gremio extended their lead at the top of Group Seven with a 3-0 win over Aurora, one day after firing coach Celso Roth.
Rafael Marques, Maxi Lopez and Rever shared the goals to hand Bolivians a fourth straight defeat.
Gremio have 10 points from four games, four ahead of Colombia's Boyaca Chico.
