Needing just a point to advance, Alvaro Negredo settled any nerves with his fourth goal in five internationals this season midway through the first-half.
And substitute Juan Mata sealed the three points with virtually his first touch of the ball 15 minutes after the interval.
Victory means Spain finish Group I three points clear of France and continue their remarkable record of not having lost a World Cup qualifier for over 20 years.
"In the course of the competition we have had difficulties that we had to solve by winning in Paris and then the games afterwards," Spain boss Vicente del Bosque admitted.
"We need to value what we have done in this group. It hasn't always been easy because the opponents have defended deep and made it difficult for us.
"But we have a virtue which is to keep the ball and have patience."
Del Bosque had shown his discontent with Friday's unconvincing 2-1 win over Belarus by making six changes to his starting line-up.
The return of captain Iker Casillas in goal and an international debut for Alberto Moreno at left-back were the most significant changes, but all those who came in made a positive impact in a much more vibrant display.
Negredo had a great chance to open the scoring when Giorgi Loria spilled Pedro Rodriguez's cross, but the keeper recovered well to make a brave block at the Manchester City striker's feet.
However, the waves of Spanish attacks continued and the opener arrived on 25 minutes as Moreno, Pedro and Iniesta combined before the latter squared for Negredo to prod home his ninth international goal at the near post.
Georgia then had their first opening of the match as Nikoloz Gelashvili accelerated past Sergio Ramos, but his fiercely hit effort was parried by Casillas and Aleksandr Kobakhidze's follow-up effort sailed over.
Negredo should have had his second of the evening before the break when he struck the outside of the post when it seemed easier to score after being set up by excellent wing play from Jesus Navas.
Any doubt over the final outcome was erased on the hour mark when Mata volleyed home a loose ball inside the area just minutes after replacing Pedro.
And the Chelsea man is hoping a return to form at club level will ensure his place in Del Bosque's 23-man squad for Brazil.
"We have done what we wanted to do in these two games. We've qualified and can now look forward to the World Cup in a relaxed manner," he said.
"Obviously it is a goal for me to be there. I need to have another good season to keep my place in the national team. It would be great to go to my second World Cup and hopefully it will have the same outcome as the first."