Estudiantes, equal with Velez on 30 points with five matches to go, went down 2-1 away to modest Tigre on Saturday.
Velez worked hard to break down a stubborn Lanus defence which finally succumbed on the hour when Alvarez stepped inside his marker to unleash a left-footed shot from outside the box on the right that beat goalkeeper Mauricio Caranta at the far post.
Caranta had made two good saves before that. He denied playmaker Maxi Moralez in the first half and in the second made a double save from forward Juan Manuel Martinez, parrying his first shot then turning away his bicycle kick from the rebound.
Arsenal are third five points behind after being held 0-0 at home by All Boys on Saturday.
At the foot of the table, Quilmes ended a run of 20 matches without victory, including six in the Nacional B division from which they were promoted, with a 2-1 home win over Godoy Cruz.
Midfielder Miguel Caneo scored Quilmes's winner in added time.
The weekend programme concludes on Tuesday night with the "superclasico", one of the world's great derbies, between River Plate and Boca Juniors at the Monumental.
So often in the past a title-decider, this clash finds both teams in the bottom half of the standings and River threatened with relegation for the first time.
However, the match is still one of the great talking points of the season with River under caretaker coach JJ Lopez after Angel Cappa was sacked a week ago while Boca's Claudio Borghi could resign if his team lose.
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