Vivas, a former Argentina national team assistant coach, had been in charge for 11 matches since November, midway through the Apertura championship, and made a bright start to the Clausura with a 3-0 win over Rosario Central two weeks ago.
However, his carefully assembled side with the major mid-season signings of strikers Claudio Bieler and Gabriel Hauche and former Argentina captain Roberto Ayala failed to gel.
"We didn't get the results and by mutual agreement Vivas ceased tonight to be the team's coach," Racing president Rodolfo Molina told the official news agency Telam.
Vivas was asked by the club directors to resign after Saturday's 1-0 defeat at Gimnasia-La Plata, Ole sports daily reported. He refused, saying he wanted to carry on with what he saw as a long-term job, so they sacked him.
Racing have turned into a basket case in the Argentine game, one of the country's so-called "Big five" clubs who were crowned South American and world club champions in 1967 but have only lifted one league title, in 2001, since.
In the relegation system in Argentina whereby average points over three years are taken into account, Racing are in grave danger of going down at the end of the season in June.
FOUR-WAY LEAD
Racing's bitter Avellaneda area rivals Independiente beat an under-strength Estudiantes 3-2 to take a share of the lead with eight points from four matches.
They are joint leaders with last year's Clausura winners Velez Sarsfield, surprise team Godoy Cruz, and Colon, who beat River Plate 1-0 at home in the Santa Fe province.
Independiente, coached by 1978 World Cup winner Americo Gallego, took a first half lead through Andres Silvera and appeared to have the points sewn up when fellow striker Dario Gandin shot them two ahead just before the hour.
But a fine goal after the restart from the edge of the box by Maxi Nunez, one of the few first-team squad regulars in Alex Sabella's side that wasn't rested for Thursday's Libertadores Cup match away to Alianza Lima, put the home side on the back foot.
The Independiente fans' anger was aroused when their defence allowed substitute Jeronimo Morales Neumann to steal in unmarked and snatch an equaliser in the 71st minute.
However, a defensive lapse at the other end with 11 minutes remaining allowed midfielder Ignacio Piatti, surrounded by three static defenders, to control a high cross in the middle of the box and shoot past Damian Albil.
Titleholders Banfield beat Lanus 2-0 at home in a one-sided "Clasico del sur," the southern suburbs derby, on Saturday to leave them on six points from three matches.
Ailing giants Boca Juniors made a series of changes with young blood coming in for old hands but did not improve and were held 0-0 at their Bombonera home by Atletico Tucuman.
