Joao Pedro Galvao's solitary strike was enough to hand Marco Silva's men all three points at the Estadio Antonio Coimbra da Mota.
The visitors knew that a maximum haul in the Primeira Liga encounter would have been enough to lift them out of the relegation play-off spot and into 13th.
And they made a solid enough start, looking assured in possession without troubling the home defence.
Estoril, too, were largely frustrated in attack, but the hosts made the key breakthrough five minutes before the break.
Galvao took ownership of a throughball before keeping his composure to slot past Matias Degra.
Pacos looked to find a foothold in the early throes of the second half, with on-loan Manchester United winger Bebe attempting to provide an attacking spark.
It was the home side who twice went close to extending the advantage, however, first Degra making a smart save to deny Bruno Lopes' effort, before Evandro wasted a promising opportunity.
In the end one goal proved to be enough for Estoril, who can still mathematically reach Europe's premier competition, though they trail third-placed Porto by six points with just three games remaining.
Pacos are now just two points above the automatic relegation spot in Portugal's top flight, and are one below 14th-placed Belenenses.
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