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.
Spain had to work hard against the ultra-defensive Asian champions who, despite drawing their opening match 0-0 against South Africa and losing this one without scoring a goal are still in with a chance of reaching the last four.
Spain, who beat New Zealand 5-0 in their opening game, top the group with six points followed by South Africa and Iraq on one and New Zealand with none.
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.
FOUR CHANGES
Spain coach Vicente Del Bosque made four changes to his starting lineup, leaving defenders Carles Puyol and Raul Albiol on the bench with midfielders Cesc Fabregas and Albert Riera.
Although their replacements Gerard Pique, Carlos Marchena, Juan Manuel Mata and Santi Cazorla all played well, they found it hard going against the well-organised but negative Iraqis who seemed happy to limit the damage to one goal.
Iraq coach Bora Milutinovic, who said on Tuesday he might field an even more defensive team than he did to gain a draw against South Africa, was true to his word.
He named a side with six defenders, while the lone striker, Alaa Abdul Zahra, usually plays as an attacking midfielder.
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.
