Spain keeper Iker Casillas saved Joao Moutinho's opening penalty then Bruno Alves hit the bar to eventually open the door for substitute Fabregas, who scored via the post.
After a lively first half when Portugal took the game to their neighbours, it got cagier with fewer chances as Cristiano Ronaldo lashed two dipping free kicks just over the bar and sent another flying over in the last minutes after a counter-attack.
Spain's Alvaro Arbeloa swept a half-volley over the bar in the ninth minute and remarkably that proved to be Spain's best chance of a disjointed performance until Andres Iniesta forced Rui Patricio into his first serious save just before halftime in extra time when they finally injected some pace and took control.
Germany play Italy in Warsaw tomorrow in the second semi-final. The final is in Kiev on Sunday.
