It looked set to be a frustrating start to La Roja's bid to make it to the finals in Brazil, as a wall of Georgian defenders repelled wave after wave of attack and the hosts even initially overcame the loss of goalkeeper Giorgi Loria to injury in the second half.
But then the visitors played a corner short to substitute Cesc Fabregas, whose low centre was swept home by Soldado. It was the perfect riposte from the Valencia striker, who was not included in Vicente del Bosque's squad for UEFA EURO 2012, to the surprise of many at the time.
The win maintains Spain's unbeaten run in competitive matches stretching back to their 1-0 loss to Switzerland in their opening game at the 2010 FIFA World Cup in South Africa.
However, this was so very nearly a huge anti-climax for a Spain side that cruised to the finals of the European Championship by winning every qualifier. The pattern of the game was like so many involving Spain in recent times, with Georgia sometimes having all 11 players back behind the ball as the visitors camped in the final third.
They had chances, with David Silva crashing a left-foot shot off the woodwork following Xavi Hernandez's lay-off just before the half-hour mark. Soon after, a Xavi effort from 25 yards was tipped over the bar by Loria, before the Barcelona playmaker found Soldado, who was denied by the Dinamo Tbilisi 'keeper.
With the scores still goalless, there was always a threat that Georgia could steal the lead with a moment of magic, and they nearly did just that early in the second half when defender Aleksandr Amisulashvili curled a shot off Iker Casillas' right-hand post.
But that was a rare moment of respite, and Georgia looked in trouble when, after a stoppage of several minutes for treatment, Loria had to be replaced.
His place was taken by Roin Kvaskhvadze, who was winning his first cap. It proved to be quite a baptism of fire for the 23-year-old, who held on for 13 minutes until Soldado finally struck to silence the home fans in a 56,000 sell-out crowd.