Argentina's most decorated team have been in dire straits for the last two years and in the local system of points averages over three seasons to determine relegation they need every win they can get to avoid the drop in May.
Former Argentina World Cup forward Ariel Ortega crossed from the left and young striker Rogelio Funes Mori headed home for a 1-0 win over Tigre, the team that crushed them 5-1 in the final match of last season.
"I like winning and more so the way we did today, at the end," said Cappa. "We deserved the victory and to have scored more goals, but I'm aware we have to improve."
River's Monumental stadium was packed with a crowd of about 70,000.
"Almeyda had a colossal performance and Ortega was decisive as always," Cappa told a post-match news conference.
Title holders Argentinos Juniors, who won the Clausura under Borghi in May, were upset 2-1 at home by Cappa's former club Huracan.
Juan Sebastian Veron netted a 71st minute penalty to give Estudiantes a 1-0 away win over Newell's Old Boys in Rosario.
Alejandro Delorte headed a goal for promoted Olimpo against Banfield after 22 seconds but the home side, who won last season's Apertura in December for their first ever title, recovered to win 2-1.
