The first-half substitute completed his double in the 90th minute to lift Libertad to a 3-2 victory at the Estadio Dr. Nicolas Leoz on Friday.
Libertad are 11 points clear at the summit after 13 rounds following Olimpia's 1-1 draw at home to fourth-placed Guarani.
Pedro Sarabia's men had won seven consecutive games at home prior to kick-off but that run threatened to come to an end when Sportivo Luqueno hit the front early.
Veteran Brazilian striker Rodrigo Teixeira was on target to give the visiting team a seventh-minute lead.
However, Sportivo Luqueno were dealt a major blow on the half-hour mark when midfielder Robert Aldama received his marching orders for a second bookable offence.
Libertad made the most of their numerical advantage, with Rodrigo Lopez restoring parity from the penalty spot five minutes before the half-time break.
Bareiro, who replaced Jorge Moreira in the ninth minute, put the home side ahead just 10 minutes after the interval.
Sportivo Luqueno equalised 12 minutes later thanks to Matias Lequi, who made no mistake from the spot.
But Bareiro struck during the closing stages as Libertad downed their eighth-placed opponents in cruel fashion.
Elsewhere over the weekend, Nacional Asuncion missed the chance to move second in the standings after they were beaten 1-0 by Rubio Nu.
Nacional Asuncion, who have a game in hand, were triumphant midweek against Arsenal in their Copa Libertadores quarter-final tie.
But they failed to produce the goods at home to Rubio Nu, with Maximiliano Lugo's 14th-minute goal proving to be the match winner.
Nacional Asuncion remain in fifth spot on 20 points, just one ahead of Rubio Nu, who rose to sixth.
Cristian Ovelar bagged a brace as third-placed Sol de America recorded their third win on the bounce, accounting for strugglers Deportivo Capiata 3-0.
In other results, General Diaz edged 12 de Octubre 1-0, who slid to the foot of the table following 3 de Febrero's 1-1 draw with Cerro Porteno.
