Midfielder Manuel Lanzini rose between Boca's central defenders to head River into the lead after 45 seconds from winger Carlos Sanchez's right cross.
Uruguayan striker Santiago Silva equalised six minutes before half-time when he steered the ball right-footed inside the far post from Walter Eriviti's square ball on the right.
"We're going with a bitter taste, we came for the three points, we lacked cool heads in front of goal," said Lanzini, whose team, unbeaten in six matches and challenging for the title, squandered several chances.
Boca, near the bottom of the 'Final' championship standings after going 11 matches without a victory in the league, had defender Guillermo Burdisso sent off for a two-footed challenge on Sanchez in the dying minutes.
River should have been two goals ahead when Silva scored for Boca but in the 35th minute Sanchez contrived to lob an easy chance the wrong side of the post after Juan Manuel Iturbe's left cross had beaten the defence.
After a 2-2 draw at the Monumental in October in the 'Inicial' championship in the first half of the season, both derbies have been drawn since River returned from relegation in 2011.
Independiente, another of Argentina's co-called Big Five clubs, won 2-0 at Tigre for their second successive victory in a tough battle to avoid relegation for the first time.
Fernandez made it two in the 40th when he raced through to hit Colombian striker Juan Caicedo's square ball on the edge of the box. Garcia parried it coming out near the penalty spot but the ball looped high and dropped into the goal just below the crossbar.
Striker Silvio Romero hit both goals for Lanus to take his tally to eight at the top of the scorers' list.
