Veteran striker Martin Palermo scored in his last big derby to leave River dangerously close to the play-off berths in the three-season relegation points averages after a third loss in four matches.
Boca's fifth match without defeat confirmed their recovery from a poor start to the championship, climbing to eighth with 21 points from 14 matches, one place and one point behind River in the Clausura standings.
Boca went ahead in the 28th minute when left-back Luciano Monzon's glancing header from Juan Roman Riquelme's corner to the near post wrong-footed Carrizo, with the ball bouncing off his thigh into the net in the 28th minute.
Less than three minutes later, the ball came high into the River box and Palermo, with Carrizo committing himself prematurely, headed over the goalkeeper into the net.
The 37-year-old Palermo, Boca's record all-time scorer whose goal was his fourth in as many games, was substituted 10 minutes from time to a huge ovation from the Boca faithful as they chanted his name.
RETIREMENT CLOSE
Palermo, now five matches from his retirement at the end of the season, took his personal tally against River to 11 in two spells as a Boca player.
"I said during the week I wanted to give the fans happiness... there's nothing that can compare with this 'clasico' and I'm thrilled to have scored in my last," Palermo told Futbol Para Todos.
"Boca's people are unique and happy we've beaten our eternal rivals," said Riquelme.
River had a chance cleared off the line by Monzon and another shot from Paraguayan left-back Adalberto Roman well saved at the near post by goalkeeper Cristian Lucchetti.
River captain Matias Almeyda, who had already been booked, and Boca defender Clemente Rodriguez were sent off for fighting in a nervy finish in stoppage-time.
Earlier, title holders Estudiantes were held 2-2 at home by Tigre to go 11 matches without a victory in the league and South American Libertadores Cup. They are eight points behind leaders Velez Sarsfield.
Libertadores Cup quarter-finalists Velez lost 3-2 at Lanus and had their lead in the standings cut to one point over second-placed Godoy Cruz, who beat relegation candidates Quilmes 2-0 on Friday. Lanus are third four points behind Velez.
