Spain books World Cup ticket with win
Spain only needed a draw to ensure they finished top of Group I ahead of France and Negredo's fourth goal in his last five appearances for his country gave La Roja a half-time lead before substitute Mata sealed the win just after the hour.
Spain coach Vicente del Bosque rang the changes following Friday's nervy 2-1 win over Belarus with only five players - Barcelona quartet Xavi, Pedro, Sergio Busquets and Gerard Pique plus Real Madrid defender Sergio Ramos - keeping their starting spots.
Among those to come in were locally-born Andres Iniesta, debutant left-back Alberto Moreno and Negredo up front, and it was the Manchester City striker who again showed his international class with an impressive showing.
Pedro was the biggest early threat to the visiting goal, drawing two stops out of Georgia goalkeeper Giorgi Loria while also firing another chance over, but then Negredo claimed center stage.
He had a shot blocked by Gia Grigalava, drilled a second effort just wide before drawing a brilliant save out of Loria in the 20th minute with an acrobatic overhead kick.
Negredo might have felt he deserved a goal for that effort, but he need not have worried as five minutes later he did get his name on the scoresheet as he stole in at the near post to stab home Iniesta's volleyed cut-back.
That was just what Spain would have wanted to prevent the tension building, but they then had to weather a brief Georgia storm immediately after Negredo's goal which saw the recalled Iker Casillas save from Jaba Kankava and Nikoloz Gelashvili before Zhano Ananidze fired over.
The save from Gelashvili showed the veteran Real Madrid keeper at his best and, with the danger averted, normal service was resumed with Spain back on the attack and Negredo again in the thick of things.
Holders Spain ensured they would be in Brazil next year to defend their World Cup title as goals from Alvaro Negredo and Juan Mata earned them victory over Georgia in Albacete.
He came within inches of making it 2-0 in the 40th minute with a close-range shot that struck the post.
The reigning world and European champions picked up where they left off in the second half, with Iniesta, Negredo and Jesus Navas trying their luck before substitute Mata made an instant impact by doubling Spain's lead in the 61st minute.
The Chelsea player had only been on the pitch four minutes after replacing Pedro when he pounced on a loose ball in the area to slam a left-footed shot past Loria.
That proved to be the end of the scoring with Spain relatively untroubled by Georgia in the closing stages as they sealed their passage to Brazil next summer.