The defender's individual strike in the opening moments of the game saw Spain on their way, and Fernando Torres struck having been on the pitch for less than two minutes. Alba completed the straightforward win in the closing stages after breaking clear of the Nigerian defence.
Alba got Spain off to the perfect start with a goal in the opening moments of the match. La Roja's No18 skipped past a number of Nigeria challenges and was left with a simple finish past Vincent Enyeama.
Cesc Fabregas should have doubled Spain’s lead just before the interval. Soldado whipped a fantastic ball across the box, but Fabregas scuffed his shot and the ball hit the post, ending up in Enyeama’s grateful grasp.
Nigeria started the second half brightly, and Ideye could not convert a promising Musa cross. The African side were made to pay for their profligacy.
Fernando Torres arrived from the bench after the hour mark and made an instant impact. Pedro received the ball on the Spanish left after some calculated build-up play and whipped a devilish ball across the Nigeria box. Torres headed past Enyeama to put him one goal behind the tournament record held by Cuauhtemoc Blanco and Ronaldinho.
Another substitute almost made an instant impact, as Gambo Muhammad was found wide open in the Spain box but his shot bounced harmlessly wide.
Jordi Alba then polished off the three points with the third goal, breaking free of the Nigerian offside trap and calmly rounding Enyeama before slotting home.
Nigeria were punished for failing to convert their chances and, with the youngest squad at the tournament, will head home hoping to return to Brazil next year having learned some valuable lessons.
Spain secured their place at the top of Group B to set up a mouthwatering semi-final against Italy, a re-match of the UEFA EURO 2012 final.