After nine straight quarters of contraction in the second trough of a double-dip recession, the eurozone's fourth-biggest economy grew by 0.1 percent, the Bank of Spain said in a report.
The rate at which jobs were being destroyed in the recession, which has thrown millions out of work and increased poverty, eased to its slowest rate since the start of the crisis in 2008, it added.
"In the third quarter, the Spanish economy extended the gradual improvement that it has been observing since the start of the year," the bank wrote.
Wednesday's data came in an economic climate "characterized by a certain easing of financial tensions and improving confidence".
The bank's quarterly estimates are usually confirmed by the government's official figures, due later this month.
The rate of destruction of jobs was 0.1 percent, which if confirmed would be "the least unfavourable rate since the start of the crisis" that erupted in 2008 with the collapse of a building boom, the bank said.
The jobless rate was a huge 26.3 percent in the second quarter, according to the latest definitive figure.
Separately the economy ministry said that Spain slashed its trade deficit in August by 42.5 percent to €1.8 million ($2.5 million).
The government has been trumpeting exports as one of the motors to drive the country out of its slump.
Exports rose by 3.8 percent compared to August last year to €17.2 billion while imports decreased by 3.6 percent.
"As the slide in domestic demand peters out, the ongoing surge in exports will drive growth" in Spain, wrote analyst Holger Schmieding of Berenberg bank.
"Over the course of next year, we look for a rebound in investment to add to the export gains."
Schmieding said the positive data from Spain reflected a general recovery in European countries hit by the financial crisis, such as Greece, Ireland and Portugal.
He said this was thanks to the supportive action by the European Central Bank last year.
"The worst is over. One by one, the euro crisis countries are returning to growth after a savage adjustment recession," the analyst wrote .
Other analysts warn that tough challenges to Spain's recovery remain, however. Unions and the political opposition say ordinary Spaniards will continue to struggle with high unemployment and public spending cuts.
"We expect private deleveraging together with tight financial conditions and the ongoing adjustment in the housing sector to continue to cap any significant economic growth in Spain in the following years," wrote analysts from Citi bank in a report .
The central bank said Spanish domestic demand declined 0.3 percent in the third quarter compared to the second, with sluggish household spending, but external demand rose by 0.4 percent.
Spain's conservative government is forecasting an overall decline of 1.3 percent output in 2013 before a return to growth of 0.7 percent over 2014.
It forecasts an unemployment rate of 26.6 percent his year and 25.9 percent in 2014.
Spain's national statistics institute publishes the official provisional quarterly growth figures on and the definitive ones on .