Spain striker Negredo fired his side ahead after 36 minutes before Ivan Rakitic doubled Sevilla's advantage.
Here Negredo creates its albums, as well as letting local kids try their hands at recording rap songs.
In the night's other tie, Sevilla cruised past nine-man Real Zaragoza 4-0 thanks to two goals from Alvaro Negredo.
Striker Alvaro Negredo scored all four goals for mid-table Sevilla as visiting Valencia dropped to fifth place despite a second-half double from forward Roberto Soldado.
The second half began in similar fashion and Negredo set up Perotti for a certain score only for Casillas to charge across his line to save.
Negredo, an old-fashioned target man, cut an isolated and slightly incongruous figure among Spain's cast of diminutive passers, and failed to exploit the space behind Portugal's high defensive line.
WSJ: Euro 2012: Spain Beats Portugal on Penalty Kicks, Stands One Win From Immortality
Negredo netted his second from the spot before Manu del Moral completed the rout to set up a last-four clash with either Atletico Madrid or fierce rival Real Betis.
Jose Angel Valdes was sent off for a second booking with 10 minutes left after Alvaro Negredo went down clutching his face, and the Sevilla forward set up defender Cala from the resulting free-kick.
Meanwhile, on the pitch, Sevilla moved up to fourth place in the table as a double from Alvaro Negredo -- the second a superb chip -- earned them a 2-1 home victory over third-placed Valencia.
Alvaro Negredo, who had played just 30 minutes at the tournament as a substitute in Spain's 1-0 group-stage win over Croatia, did little to justify Del Bosque's surprise decision to name him to the starting lineup.
WSJ: Euro 2012: Spain Beats Portugal on Penalty Kicks, Stands One Win From Immortality
Thus, apart from Villa, the only genuine striker included in the squad for these qualifiers was Alvaro Negredo, a fine player but also one whose club, Seville, is stuck in mid-table and who, at 27, probably won't make much more progress.
Spain followed in the footsteps of countries such as West Germany in 1982 and the Netherlands this year by winning all their qualifying matches, sweeping aside the second-best team in their pool thanks to early goals from Gerard Pique and David Silva and two in the second half from Alvaro Negredo on his first start for his country.
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