Led by captain Mayer Candelo, Millonarios had few problems overcoming Itagui to rise to 21 points from 11 matches and claim second position in the table.
Millonarios leapfrogged Once Caldas and Santa Fe (both 20 points), while Nacional occupy top spot in the standings with 25 points.
Candelo played a role in all three of Millonarios' goals on Sunday, providing the final pass to the latter two.
The 37-year-old attacking midfielder was part of a crisp move on the left-hand side of Millonarios' attacking penalty area in the 13th minute, which culminated with Alex Diaz smashing the ball past Itagui goalkeeper David Gonzalez.
Itagui kept giving the home side too much space through the middle and on the stroke of half-time, Candelo burst forward with the ball at his feet, before feeding Dayro Moreno, who toe-poked his shot under Gonzalez.
In the 77th minute, Candelo teed up Harrison Otalvaro for Millonarios' third goal after the 28-year-old midfielder was allowed to run unmarked through the middle of Itagui's defence.
Sunday's win was Millonarios' third in a row in the Primera A and extended their unbeaten run to eight matches.
With Nacional held to a 1-1 draw by Deportivo Pasto on Friday, Millonarios edged closer to the league leaders.
Once Caldas drew 1-1 at Boyaca Chico to drop to third, while Santa Fe defeated La Equidad 2-0 on Saturday to temporarily sit above Millonarios, before the latter's win on Sunday.
Uniautonoma extended Medellin's misery at the bottom of the table, winning 4-2, while Deportes Tolima cruised to a 3-1 win over Junior, Envigado defeated Atletico Huila 2-0 and Deportivo Cali triumphed 2-1 over Patriotas Boyaca.
In the other match of the weekend, Alianza Petrolera edged out Fortaleza 1-0.
