Disney (DIS) shares rose 5% Wednesday, a day after the giant media and theme-park company blew away Wall Street’s fiscal first-quarter earnings expectations. One eye-opener in Disney’s report was the strong performance of its theme park business. Revenue there rose 11% from a year ago, and operating income surged 25%, as guests continued to flood through the gates of the Disney resorts around the globe.

If a slowing economy and high energy prices are forcing U.S. consumers to be stingier, how can theme park results be so strong? Clark Dodsworth, a San Francisco entertainment and technology consultant, sees many answers. He says Disney’s theme parks do a strong repeat business because the company continually rolls out new attractions. He adds that when recessionary conditions cause some consumers to cut back on travel, people who live near the company’s parks in California and Florida become more apt to visit. And don’t forget, a weak dollar is boosting foreign tourism as well, he says.

Dodsworth points to one other factor behind Disney’s success: the company’s years of experience in branding, combined with growing efforts to harness the power of new technology. He cites Disney’s Pal Mickey, a stuffed-mouse toy that “will let you in on insider park tips, give you parade and showtime reminders, tell you when your favorite characters are nearby, and let you know about short waits at your favorite attractions,” Disney’s web site advises. Even if that sounds like too much information, Dodsworth says Pal Mickey reinforces an important point about the company. “Disney knows how to get your attention,” he says.

If there’s a recession, Disney (DIS) isn’t seeing it. The media-and-theme-parks giant roared past Wall Street’s estimates Tuesday evening, posting a 29% rise in comparable per-share earnings. Disney made $1.25 billion, or 63 cents a share, for the fiscal first quarter ended Dec. 29, compared with the year-ago $1.7 billion, or 78 cents a share. Excluding a gain in last year’s quarter tied to Disney’s sale of equity investments in E! Entertainment and Us Weekly, earnings rose to 63 cents from 49 cents a year earlier, handily beating the 52-cent analyst consensus estimate. Revenue rose 10% from a year ago in media networks and 11% in parks and resorts, while the studio entertainment unit posted flat revenue.

“We’ve started off 2008 with another outstanding quarter, marked by strong creative and operational performances,” said CEO Robert A. Iger, who recently signed a new five-year contract. “These results once again highlight the quality of our content and our unique ability to leverage it across our many businesses and territories.” Disney shares surged 4% in late trading, more than reversing the stock’s Tuesday afternoon decline. The solid results hark back to a comment Iger made last fall, when recession worries were starting to pick up.

“People have not stopped or slowed down when it comes to taking family vacations,” Iger said at a September conference, Bloomberg reports. “Some people will keep the family vacation and not replace a faulty refrigerator. That’s an interesting phenomenon.”  And, for Disney, a profitable one.