Talented midfielder Lanzini finished off a brilliant attack involving Colombia's Teo Gutierrez and striker Fernando Cavenaghi but former River forward Carlos Luna hit back with a header on the half hour.
Estudiantes, who won 1-0 at All Boys on Saturday, have six points from two matches in the second of the two championships in the season with River, Velez Sarsfield, Olimpo, Atletico Rafaela and Rosario all on four.
Playmaker Juan Sebastian Veron, who has said he will quit at the end of the season in May having come out of a previous retirement in 2012, was fit to start for Estudiantes after injury problems.
"I needed to make a comeback and thanks to the 'prof' (physical trainer) I had good preparation and also thanks to the coaching staff. I'm happy to be back," the 38-year-old Veron told reporters.
Title holders San Lorenzo beat Racing Club 1-0 at the Nuevo Gasometro, recovering from a poor start to the year during which they had lost two away matches at Olimpo in the league and to Brazil's Botafogo at the Maracana in a South American Libertadores Cup group match.
"We were the San Lorenzo of last year," said midfield general Juan Mercier of an improved performance by the Saints rewarded with a goal by former Boca Juniors striker Nicolas Blandi.
"If you lose two matches in a row there is talk of things not going well ... (but) the crowd's support was incredible, it didn't look like we'd lost two matches."
Former Lazio striker Mauro Zarate scored twice early in the second half to inspire Velez to a 3-1 victory at Copa Argentina winners Arsenal.
Copa Sudamericana holders Lanus, who like Newell's Old Boys and Velez were in with a chance of the title until the last day of the Inicial championship in December, fell 3-0 at home to Rafaela.
Newell's lost 3-0 at Gimnasia in La Plata, their 10th consecutive match without a win.
- Sports & Recreation
- Velez Sarsfield
- Juan Sebastian Veron
- Fernando Cavenaghi
- Carlos Luna