* Adjusted profit $1.04 a share vs estimate of $1.03
* Revenue falls short of analysts' estimate
* Shares up over 3 pct in early afternoon trade (Adds analyst, company comments)
July 23 (Reuters) - Delta Air Lines reported a higher-than-expected second-quarter profit as it flew fuller planes and enjoyed higher passenger revenue in the United States, boosting its shares by 3 percent.
Atlanta-based Delta has bolstered revenue by charging more for seats with greater legroom, replacing 50-seat regional jets with larger, more cost-efficient planes.
The airline also said its Pennsylvania refinery, which it bought in 2012 to help reduce fuel expenses, turned a profit in the second quarter.
Solid financial performance has positioned Delta to be able to pay down debt, raise its dividend and buy back stock as it builds on a strategy to enhance returns for shareholders.
"Delta seems to be hitting on all cylinders internationally and domestically with well-controlled costs and finally getting benefit from its refinery," said Jim Corridore, an analyst with S&P Capital IQ.
"In every aspect of the way it is operating - cash flow generation, debt repayments, stock buybacks - it seems to be doing everything right," he added.
The airline said it expected unit revenue - a benchmark industry gauge known as passenger revenue per available seat mile - to grow 2 percent to 4 percent in the current quarter. That metric surged 5.7 percent in the just-completed quarter.
Delta forecast operating margin, a measure of profitability, of 15 percent to 17 percent for the current quarter; that compares with 15.1 percent for the second quarter.
"As we look into the fall, we see good forward bookings and all signs point to a continued solid demand environment," Delta President Edward Bastian said during a conference call.
Delta's second-quarter net income totaled $801 million, or 94 cents a share, compared with $685 million, or 80 cents a share, a year earlier.
Adjusted for restructuring and other items, profit was $1.04 a share in the latest period, compared with the $1.03 expected by analysts on average, according to Thomson Reuters I/B/E/S.
Revenue rose 9 percent in the quarter to $10.62 billion, compared with analysts' forecast of $10.65 billion. Passenger revenue rose 15.7 percent in the United States and 5.5 percent in Europe, and Delta cited a strong performance at its Atlanta and New York hubs. Yields weakened, however, in Asia and Latin America.
Delta also said oversupply was a challenge in Europe, but added that joint ventures such as the one it has with Britain's Virgin Atlantic Airways was helping it draw more corporate customers. Demand in Latin America was picking up after weakness tied to World Cup soccer matches, it said.
Shares of Delta jumped 3.1 percent to $38.86 as other major U.S. airlines gained. Delta's stock is up 41 percent so far this year, compared with a 70 percent rise for American Airlines Group and a 21 percent rise for United Airlines. (Reporting by Karen Jacobs in Atlanta; editing by G Crosse, Franklin Paul and Bernadette Baum)