Adolfo Holguin's men ensured the top-flight cellar-dwellers remained point-less through seven games, with goals to Dairon Asprilla, Sebastian Herrera and Ayron Del Valle.
Asprilla saw the hosts at Estadio Alvaro Gomez Hurtado ahead inside 100 seconds of kick-off, his effort from the right powering into the top left corner of Diego Novoa's goal.
Herrera doubled Alianza's lead in similar fashion, released on the right channel but kept his finish low as he scored past the right hand of the stranded Novoa.
La Equidad pulled one back in the 51st minute, when Deiver Machado got the final touch into his own net, deflecting in a cross in from the left for the visitors.
Del Valle ensured Alianza of the three points late on, his 86th-minute effort inflicting more misery on the bottom club.
La Equidad were also humbled earlier in the week, suffering a 4-0 home loss to Atletico Nacional.
Junior won a seven-goal thriller at home to Atletico Huila in mid-week, triumphing 4-3 after twice coming from behind.
Jhonny Vasquez and Andres Correa scored first-half equalisers for Junior, before Jarlan Barrera put them ahead four minutes after the interval.
Atletico made it 3-3 10 minutes later courtesy of Juan Caicedo's effort, before Luis Quinones scored the winner in the 70th minute.
Aguilas Doradas snapped a two-match losing run, beating Santa Fe 2-1.
