Soldado, back in the world and European champions' squad after a five-year absence in place of the struggling Fernando Torres, made the most of his chance to impress coach Vicente del Bosque after coming off the bench for the second half.
The Valencia striker also missed a 66th-minute penalty after he was hauled down in the area by defender Fernando Amorebieta, his tame effort easily saved by goalkeeper Daniel Hernandez.
Venezuela had their backs to the wall after the dismissal, which occurred when they were 4-0 down, but had done well to keep the dominant Spaniards at bay until the 37th minute at Malaga's Rosaleda stadium.
Fabregas sent Iniesta clear to score the dramatic extra-time goal that beat Netherlands 1-0 in the 2010 World Cup final and it was his low centre that his Barcelona team-mate turned into the corner of the net for the opener.
The home side doubled their lead three minutes later when David Silva sped into the area from the right, exchanged a quick pass with Fabregas and drilled the ball into the far corner.
Soldado, who made his two previous appearances for Spain in 2007, opened his account for the national side five minutes into the second half when he flicked a Santi Cazorla pass into the net from close range.
He grabbed his second three minutes later when he turned in Alvaro Arbeloa's low cross and made amends for the missed penalty six minutes from time when he lifted a Jordi Alba cross high into the net to complete his hat-trick.
"It's a dream to return to the national team in this way, but you also have to take into account the circumstances in the second half, which was even worse for them with the sending off," Soldado told Spanish television.
"Also I can't forget the penalty I missed," he added.
"I don't think [this hat-trick] is my ticket to the Euros. I think it was an opportunity, but there are still three months of competition to go and this will go a long way to deciding if I go to Euro 2012 or not."
The match against the 2011 Copa America semi-finalists was a last chance for coach Vicente del Bosque to experiment before he names his roster for the European Championships and he started with Fernando Llorente as a lone striker in the absence of Torres and the injured David Villa.
Llorente sent a couple of tame headers goalwards in the first half but was otherwise quiet and was comprehensively upstaged by Soldado, who replaced him at the break.
Venezuela barely threatened Spain's goal, their best chance coming as early as the third minute when Jose Salomon Rondon's fierce strike was beaten away by Iker Casillas.
The home side's mesmerising one-touch passing and solid defence easily kept the South Americans at bay as Spain, playing in a new and unfamiliar sky-blue strip, celebrated their 600th match with a thumping victory.
"It's fair to say that we met all our objectives for tonight's match," Del Bosque told a news conference.
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