DETROIT — Auto sales defied a downcast economy in September, climbing 9.9 percent to their highest level in five months as new models arrived at dealerships and inventory shortages eased.

All three of the Detroit automakers reported gains, led by a 27.2 percent year-over-year increase for Chrysler, which outsold Toyota for the fourth time this year.

Toyota and Honda again trailed the rest of the industry, even though September was the first month since the March earthquake and tsunami in Japan that all of their plants were running at full capacity. Toyota’s sales dropped 17.5 percent, and Honda’s were down 8 percent. In contrast, Nissan sales increased 25.3 percent.

The industry’s seasonally adjusted, annualized selling rate rose to 13.1 million, the first time since April that they had exceeded 13 million. General Motors and Ford Motor each said they still expected total sales for 2011 to top 13 million, which would require demand to jump further in the fourth quarter.