Teenage substitute Federico Andrada headed the only goal in his third top flight appearance to give River the victory over promoted Central in the Argentine "Inicial" championship.
River, playing poorly at the Monumental, scored from a corner 12 minutes from time when Andrada headed home at the far post.
Two minutes later River found themselves down to 10 men after midfielder Jonathan Fabbro was shown the red card on his debut for a nasty foul.
Paraguay international Fabbro was sent off for striking Pol Fernandez in the face with his boot as the Central player headed the ball out on the wing.
Coach Ramon Diaz's side had lost 1-0 to Gimnasia-La Plata, another promoted team, in their opening match of the season last weekend.
Diaz, who made attacking substitutions midway through the second half to try to unlock the Central defence, admitted his team had played poorly but said he thrived on pressure from the home crowd.
"This is River and you've got to play well. The public put pressure on us but we also have a lot of courage... We needed the points and went looking for them," he told reporters.
Winning was a relief for Diaz who is keen to slot Gutierrez into his rebuilt side for a tilt at the title.
Cruz Azul issued a statement on Friday demanding Gutierrez return to Mexico and report for training on Monday after the transfer fee from River had not come through.
Diaz said: "Teo is desperate to play (for River), he keeps telling everyone that."
The only team with a maximum six points after two rounds of matches are Juan Antonio Pizzi's San Lorenzo, impressive in a 3-0 away win over Racing Club but unseen by fans.
Racing had to stage the game behind closed doors after their Cilindro stadium was suspended for one match following crowd trouble.
Uruguayan striker Martin Cauteruccio took his tally to three in two matches since joining San Lorenzo from Quilmes in the close season.