The comfortable victory in Helsinki stretched the world and European champions' lead over France at the top of the group to three points with two matches remaining after the French could only manage a 0-0 draw against Georgia in Tbilisi.
Cesc Fabregas chipped the ball over the stubborn Finland defence in the 19th minute at a packed Olympic stadium and Alba took one touch before firing between the legs of goalkeeper Niki Maenpaa.
As Finland pressed further forward late in the game, Xavi released Jesus Navas on the right four minutes from time and he squared the ball to fellow substitute and Manchester City team mate Negredo who clipped it high into the net.
Finland, who are third in the group, five points behind France, came closest to scoring in the 12th minute when Iker Casillas saved with his feet after the ball bounced off team mate Sergio Ramos.
Spain play their final two qualifiers at home to Georgia and Belarus next month.