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SAN FRANCISCO — Just because Gap Inc.’s sales rose for the first time in 2 1/2 years doesn’t mean the long-slumping retailer finally has turned the corner, company executives and industry analysts said Thursday. 

Gap raised hopes for better times by reporting October sales that far exceeded expectations. The San Francisco-based company’s same-store sales — a key measure of how a retailer is faring compared to the previous year — climbed 11 percent in October. 

The surge ended 29 consecutive months of declining same-store sales at the Gap. Spurred by a catchy advertising campaign tied to the “Green Acres” theme song, the Gap’s discount chain — Old Navy — fueled the comeback with a 24 percent increase in same-store sales. 

Business rebounded so much during October that Gap said its third-quarter profit will be at least two times higher than investors previously expected. 

Gap expects to earn 12 cents to 14 cents for its just-completed fiscal quarter, well above the previous consensus estimate of 6 cents among analysts surveyed by Thomson First Call. 

Investors cheered the news. Gap’s shares climbed 65 cents Thursday to close at $13.42 on the New York Stock Exchange. 

“The company is really starting to make things happen again, but it’s still too early to declare victory,” said industry analyst Richard Jaffe of UBS Warburg. 

Gap management isn’t ready to celebrate yet, either. 

“While we are pleased with October’s results, our outlook remains cautious until we see more consistent performance over time,” said Heidi Kunz, Gap’s chief financial officer.