Forward David Villa's powerful 55th minute header made him Spain's second highest scorer of all time with 30 goals - 14 behind Raul's record of 44.
It was his fifth international goal in a week following a hat-trick against Azerbaijan last Tuesday and another strike against New Zealand on Sunday.
But this match was in stark contrast to the New Zealand rout and until the unmarked Villa headed in Joan Capdevila's cross 10 minutes after the break it looked like Spain would fail to score for the first time since a 0-0 draw with Italy in Euro 2008.
The defensive tactics stifled Spain's attacking prowess and killed the game as a spectacle with the favourites continuously frustrated by the sheer weight of numbers defending.
Iraq only managed one shot on target in the first half when Zahra fired tamely at goalkeeper Iker Casillas after 10 minutes, while Spain's best efforts went wide and striker Fernando Torres was left to feed on half-chance scraps he failed to convert.
Defender Sergio Ramos nearly doubled Spain's lead with a blistering shot that went just over the bar after 78 minutes.
But in the end they did just enough to join Brazil, France and Australia as one of only four countries to win 14 successive matches according to FIFA's official statistics.
South Africa face New Zealand in Rustenburg in Wednesday's late Group A match.
