The victory on Saturday kept the Blue Machine fourth in the Clausura standings with eight points, four behind joint leaders Tigres UANL and title holders Tijuana who are both on a maximum 12 points.
Argentines Cristian Gimenez, with a diving header, and Mariano Pavone, with a penalty, gave Cruz Azul a two-goal lead in the first half with substitute Gutierrez scoring the third in the 51st minute and Javier Aquino adding the fourth.
The talented but controversial Gutierrez, who ran into trouble with team mates at Racing over his hot-headed reactions to refereeing decisions that earned him red cards, came on in the second half and within six minutes had found the top corner of the net.
Tijuana, winners of the Apertura championship in December, beat Pachuca 2-0 at home and Tigres won 2-0 at Queretaro, while Azteca-based giants America lost 2-1 to Atlas in Guadalajara and are third with nine points.
Argentine former Cruz Azul striker Emanuel Villa, who hit a hat-trick on his debut for Tigres three weeks ago, is top of the scorers list with five goals after putting his side ahead in the first half with a fine solo effort before laying on a late second for Brazilian Danilinho.
Struggling Guadalajara, with three points from their four matches, are still looking for their first win under coach Benjamin Galindo after a 1-1 draw at Morelia on Friday.
Mexico striker Rafael Marquez Lugo put Guadalajara ahead with his second goal since returning from a long injury layoff last weekend but, after the visitors had Kristian Alvarez sent off near the hour mark, Joao Rojas snatched an equaliser in added time.