The league leaders had scored just 12 goals in their first nine league matches, with their defence - only four goals conceded - seeing them remain undefeated.
But Rivero's sending off after just five minutes allowed Guillermo Sanguinetti's men to open up the visitors to the Estadio Alejandro Villanueva.
Pablo Miguez doubled Alianza's lead in the 32nd minute, nodding home from a cross, before he bagged a brace 10 minutes later - lashing home a left-foot volley after Miguel Araujo pulled a ball back into the danger area from the right byline.
Walter Ibanez made it 4-0 just prior to half-time, converting a spot kick straight down the middle of the Cienciano goal, while Mauricio Montes was on hand to tap home Alianza's fifth on the hour mark, sliding in at the back post after Victor Cedron missed Gabriel Costa's cross.
Sergio Blanco's first-half brace helped set up a fourth straight victory for Daniel Ahmed's men.
Janio Posito's quick-fire brace late on helped Los Caimanes to a 3-2 win away at Cesar Vallejo, catapulting the victors to 10th.
