The Blue Machine ended a winless run of 11 matches, stretching back to last season, and left the Pumas bottom of Group Three with no points from two games after last week's 1-0 defeat at Atlas.
Pumas, coached by Brazilian Ricardo Ferretti, fell behind just before halftime when their Paraguayan defender Dario's Veron headed back pass sailed over goalkeeper Sergio Bernal into his own net.
Cruz Azul's Paraguayan midfielder Cristian Riveros increased their lead early in the second half with a header from Jaime Lozano's cross.
Argentine striker Emanuel Villa, who joined Cruz Azul from English Championship (second division) side Derby County at the end of last season, netted the third after picking up a rebound off keeper Bernal.
There were big victories for Tigres UANL, who won 3-1 at Guadalajara, and Monterrey, who beat former Mexico coach Ricardo La Volpe's Atlas 3-0.
The only teams with 100 percent records after two matches are Toluca, 2-0 winners away to Chiapas on Saturday, and Pachuca, who beat promoted Queretaro 3-1 on Friday.
CONCACAF club champions Atlante's game with San Luis was postponed because they have been taking part in the Peace Cup tournament in Spain.
'People will remember us because we got to No.1 in the world rankings and achieved great things - but our biggest regret is that we didn’t win anything': Ex-Everton star Kevin Mirallas opens up on 'honour' of being part of nation's golden generation
‘I’m sure we’d have finished in the top four or five if he hadn’t joined Chelsea in January. Him leaving damaged the team, but we couldn’t stand in his way’: Alan Curbishley reflects on failed Champions League dream after selling key player
