Henry Rojas was picked out in the left side of the area, and after taking a touch, he tucked away the opening goal with his left foot in the 24th minute.
The then cellar-dwellers were 2-0 up when Ayron del Valle was on hand to tap in from point-blank range four minutes into the second half, after a low cross in from the left.
Yessi Mena pulled one back for the hosts in Itagui with eight minutes to play, striking a first-time shot from the edge of the penalty area.
But the goal would be in vain, as Alianza made it two wins from their past three matches to relegate Deportivo Cali to the foot of the table.
Cali picked up a point on the road at Fortaleza in a 0-0 draw, a result which did neither of the struggling clubs a favour.
Patriotas Boyaca moved into the top eight, with a 1-0 home win over Medellin.
Jonathan Estrada struck the game's only goal on 37 minutes, to send Boyaca to their second straight win and into eighth spot.
Atletico Huila climbed into 12th, following a 2-0 win at home to Deportes Tolima.
Hernan Hechalar's penalty put Huila ahead on 32 minutes, before Cesar Valoyes doubled their lead with 18 minutes to play.
Millonarios had an invaluable 1-0 win away at Junior, with the points taking them to third in the table.
Mayer Candelo's goal ensured Millonarios' unbeaten streak stretched to seven matches, and put them within six points of league leaders Atletico Nacional.
Once Caldas failed to cut the gap on Atletico Nacional, with the second-placed side held to a 0-0 draw at home to La Equidad.
Boyaca Chico snapped a two-match losing run, as they held Deportivo Pasto to a 0-0 draw on the road.
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