Title holders Velez beat Godoy Cruz 2-0 to move to 24 points from 12 matches, a point ahead of four teams including San Lorenzo, who were held 2-2 at Gimnasia-La Plata. Struggling Racing have eight points.
Racing Club, turned down by Lothar Matthaus for the coaching job in midweek and playing under caretaker coach Juan Barbas for the fourth match, did their fight to avoid relegation a power of good with the win.
Barbas, who before the game urged the club to choose a coach as soon as possible, told reporters after the final whistle: "I'd like to stay on but the directors have the last word".
Racing's first two goals came in the opening 12 minutes and were scrambled home by Pablo Luguercio (pictured) and Pablo Caballero.
The third, in the 34th minute, was helped in by Atletico defender Lucas Desvaux after midfielder Adrian Lucero shot following a one-two with Matias Cahais.
The fourth goal came midway through the second half, Luguercio turning his marker and crossing low for Lucas Aveldano to blast into the net.
Tucuman had Desvaux sent off five minutes from time.
Diego Simeone's "Saints" looked set to take top spot leading Gimnasia 2-1 in the final minute but they were to rue missing three golden chances to secure all three points.
With play flowing from end to end, a Bernardo Romeo effort was kicked off the line and keeper Gaston Sessa made two saves before Paraguayan defender Ruben Maldonado headed Gimnasia's equaliser from a corner.
