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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.
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.
