River scored a late equaliser through central defender German Pezzella for a 1-1 draw away to Colon at the 'Elephant's Graveyard' in Santa Fe that denied the home side the victory that would have put them top.
Viatri took his championship tally to three with goals in each half including the 69th-minute winner at La Bombonera. In between, Sebastian Carrera had equalised for the visitors.
Boca have 12 points from four successive wins after losing their opening match of the season.
They are one point ahead of title holders Arsenal, Newell's Old Boys and Colon.
Striker Ruben Ramirez put Colon ahead with a diving header midway through the second half but Pezzella ghosted in behind the defence in the 89th minute to equalise with a low shot from midfielder Leonardo Ponzio's lobbed pass into the box.
Newell's are also gunning for the title under their former midfielder Gerardo Martino, who has returned from steering Paraguay to the 2010 World Cup quarter-finals and 2011 Copa America final.
With winger Maxi Rodriguez and defender Gabriel Heinze also back at the club, unbeaten Newell's have won three matches including Saturday's 1-0 victory over Estudiantes.
Americo Gallego made a losing start in his third spell as Independiente coach, having taken over from Christian Diaz who resigned last weekend, and said he detected signs of a lack of proper fitness in his players.
Independiente, beaten 2-1 at Godoy Cruz, took the lead through defender Cristian Tula but conceded goals in the dying minutes of each half, both scored by midfielder David Ramirez, whose winner from the penalty spot came in the fourth minute of added time.
"As a player and coach, it's always been clear to me that matches last 95 minutes, and they [Godoy Cruz] scored in the 46th minute of the first half and 49th of the second. We have to work to prevent that kind of thing," Gallego told reporters.
The record seven-times Libertadores Cup winners remain in serious danger of relegation after taking two points from their five matches.
Union's Frank Kudelka became the second coach to quit this season after Friday's 3-1 defeat at All Boys, their fifth in five matches, left them rooted to the bottom of the standings.
