The victory at Estadio Dom Afonso Henriques marked just the fifth time this campaign that Jorge Costa's charges have emerged with a maximum haul in Portugal's top flight.
The early indications were that Pacos' poor season would continue as Andre Andre opened the scoring in the 12th minute from the penalty spot, yet the visitors ensured the scores would be level at the break thanks to Bebe's equaliser.
With the game nearing a conclusion it looked as though both teams would have to settle for a share of the spoils, but Sergio Oliveira secured a huge three points for Pacos in the 84th minute.
Pacos now leapfrog Olhanense and Belenenses into 14th position, with the latter two sides in action on Sunday.
Estoril's hopes of playing European football next season were further boosted in a 1-0 triumph over Maritimo at Estadio Antonio Coimbra da Mota.
The only goal of the game was scored in the 11th minute, with Joao Pedro Galvao notching his sixth goal of the season.
Estoril retain fourth spot, which would be enough to secure UEFA Europa League qualification, while the gap to third-placed Porto and Champions League football is just four points.
Gil Vicente still have to work to do to ensure their Primeira Liga safety following a 2-1 defeat to Rio Ave at Estadio Cidade de Barcelos.
Ruben Ribeiro put the visitors ahead after 20 minutes, and the scores remained the same until half-time.
Hugo Vieira levelled proceedings from the penalty spot for Joao de Deus' men, yet the home side conceded late as Ukra kept his composure to score a spot-kick of his own in the 88th minute.
