Gorka Guruzeta and Dani Garcia also scored for Athletic at San Mames Stadium to end their brief winless run, and move into the top four in the standings.
The 23-year-old Sancet earlier on Friday was included in the squad by Spain coach Luis de la Fuente for upcoming European Championship qualifiers.
The midfielder sealed Bilbao's victory in the 81st minute after Guruzeta scored in the 10th and Garcia in the 63rd.
Athletic were coming off two disappointing setbacks — conceding a late equaliser in a 2-2 draw against Getafe at home and a 3-0 loss at Real Sociedad in the Basque Country derby.
The win moved Bilbao two points behind third-placed Girona and one point ahead of fifth-placed Atletico Madrid, who have two games in hand.
Almeria, who had only one shot on target, remain the only team without a win in the Spanish league after nine rounds. They had drawn two of their last three matches, including when they relinquished a three-goal halftime lead in a 3-3 draw at home against Granada last time out.
Athletic have won 10 of their last 11 league matches against Almeria, including the last six at home.
The Basque Country club are unbeaten at San Mames since a 2-0 loss to Real Madrid in the season opener.
Madrid have a one-point lead over defending champion Barcelona. The Catalan club visit second-to-last-place Granada on Sunday, while Madrid host 10th-placed Osasuna on Saturday.
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