La Roja rounded off their World Cup 2014 qualification campaign with a routine win at the Estadio Carlos Belmonte.
The world champion went into the match needing only a point to finish ahead of France, but never looked like dropping points on its way to a comfortable win.
Georgia was under pressure for almost all of the match and substitute Juan Mata secured the win for Spain just after the hour mark, extending Del Bosque's unbeaten run in competitive home matches to 13.
The Spain coach made six changes from the narrow 2-1 win over Belarus on Friday, including returns for Iker Casillas and Andres Iniesta, while Alberto Moreno made his debut at left back.
The home side dominated proceedings early on, with Negredo going close on two occasions in the first 25 minutes as he shot straight at the goalkeeper from close range and then saw his overhead kick tipped over the crossbar.
Negredo's persistence paid off eventually, however. Iniesta, playing in his home town of Albacete, got to the by line and played a low pass into the danger area which Negredo clipped home.
Georgia should have equalized a few minutes later as Casillas parried Tornike Okriashvili's shot into the path of Nikoloz Gelashvili, but the forward fired over the open goal.
Luck was on Georgia's side just before halftime when Negredo hit the post from close range, and Guram Kashia was there to clear his resulting header off the line.
Unsurprisingly, Spain's superiority continued into the second half, but the team found the Georgia defense tougher to break down before eventually doubling the lead.
Aleksander Amisulashvili attempted to clear a cross from the left, but he headed the ball straight at Gerard Pique and Mata lashed the ball into the bottom corner, three minutes after coming on.
With 22 minutes to play, Iniesta would still have been hopeful of getting a goal of his own and he produced a good effort with his left foot that was deflected over.
Mata was also finding space and he nearly set Navas up in the 72nd minute with a low cross to the back post, but the Manchester City forward was crucially tackled at the vital moment.
Although the home side pressed for more goals, ultimately it settled for a two-goal win as it booked passage to the finals in Brazil next year.