With Medellin losing 3-2 against Junior, a win would be enough for Itagui to leapfrog into eighth position - the last qualifying spot for the finals series.
Jhonny Mesa's 54th-minute strike secured the three points for Itagui with their job being made easier by the red card given to Pasto's John Jairo Montano in the 46th minute.
Santa Fe pegged back Atletico Huila three times before eventually going down 4-3 in a pulsating contest.
All goals came before the 65th minute as Santa Fe equalised within 10 minutes each time Huila went ahead in the first half.
Huila striker Luis Paez scored a brace with his penalty midway through the second half proving to be the match-winner.
First-placed Atletico Nacional suffered a 2-1 loss at home against Cucuta Deportivo with their focus on the semi-final stage.
Leonardo Castro scored Cucuta's winner on 80 minutes.
In other matches, Millonarios won 1-0 at Alianza Petrolera, Deportes Quindio overcame Boyaca Chico 2-1 and Deportes Tolima triumphed 3-1 against La Equidad.
Once Caldas claimed a 1-0 victory at Patriotas Boyaca and there was a 1-1 draw between Deportivo Cali and Envigado.
