Boca's victory ensured their bitterest rivals River Plate, who won 1-0 away to Quilmes, joined Estudiantes at the top of the standings with 15 points from eight matches.
Estudiantes and River are one point ahead of Godoy Cruz, who beat Huracan 3-1 in Mendoza, Velez Sarsfield, who won 2-1 at Olimpo on Saturday, and unbeaten Argentinos Juniors, 2-0 winners at Banfield on Friday.
Unmarked Uruguayan striker Rodrigo Lopez gave Estudiantes an early lead when he shot first time past stranded goalkeeper Cristian Lucchetti before Juan Roman Riquelme equalised with a brilliant free kick in the 16th minute, when he curled the ball over the wall packed in front of the goal and past a diving Agustin Orion.
"Whenever I take a free-kick I have the feeling I can score, otherwise I'd let another (player) take it. I'm in luck," Riquelme told "Futbol para Todos".
Boca coach Julio Cesar Falcioni's gamble of sending on two fresh forwards near the end paid off when substitute Pablo Mouche's cross from the right found Viatri, who leapt between two defenders to head the winner in the 90th minute that sparked wild celebrations in the Bombonera stands and terraces.
Boca now have 10 points having made a poor start to the championship. It was their first win at the Bombonera and they had only scored one goal in their previous three home matches.
River's goal in the 14th minute at Quilmes came from one of the best moves of the season involving seven touches.
The ball was played across the face of the Quilmes defence to the right where teenager Erik Lamela took a return pass as he entered the box and chipped over the goalkeeper with right-back Paulo Ferrari diving to head the ball in.
The pick of the goals on Saturday was Velez's winner at Olimpo. Midfielder Ricardo Alvarez, who had scored their first, had a shot blocked but left-back Emiliano Papa was on hand to tap the ball in at the far post.
Also on Saturday, Racing Club went down to their third consecutive defeat and had two players sent off at home in a 2-1 defeat by Tigre.
Independiente, down to 10 men from the 56th minute, ended a run of 22 matches in the league without an away win when Cristian Pellerano scored three minutes into added-time to give them a 2-1 victory at relegation-threatened Gimnasia in La Plata on Friday.
Defender Carlos Matheu was sent off for a second yellow card offence.
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