So much for lingering doublts about Toyota's (TM 0.15%) recovery: Japan's biggest automaker reported net income of 257.9 billion yen ($3.2 billion) for the quarter ended Sept. 30.

It was another solid quarter, one driven primarily by big earnings in Toyota's home market of Japan that hit a four-year high at 143.7 billion yen, or $1.8 billion. That was 46% higher than the average analyst estimate  per Bloomberg, a strong result in arguably Toyota's most important market.

But not all was rosy for the Japanese giant, as trouble in China continued to weigh.

Cost cuts and strength in Japan drove good results
Like most of the big global automakers, Toyota has been on a mission to reduce its costs in recent months, following the example of Ford (F 2.14%) and other automakers in sharing more parts between models and seeking efficiency increases throughout its organization.

Those changes have already started to add up. Toyota said that cost savings added 160 billion yen to its bottom line during the quarter and were a big part of its profit in Japan. Toyota's third straight quarterly profit in its home market (after eight quarters of losses) was also aided by Japanese government subsidies for fuel-efficient cars that helped drive strong sales of the Prius hybrid.

Results overseas were less glowing, however. Toyota has been hit hard by a wave of anti-Japanese sentiment in China, which stems from a dispute over a group of islands claimed by the governments of both countries. The company said on Monday that it expects its sales in China during its fiscal second half (Toyota's fiscal year ends on March 31) to come in some 200,000 vehicles lower than expected, costing it 30 billion yen in profits.

Toyota has cut its production in China significantly in the wake of the protests. According to a Bloomberg report, the company's internal research suggests that production is unlikely to be fully restored until next summer. Toyota's sales in China were down 49% in September and fell 44% in October versus year-ago totals.

Still leading the global sales chase
But unlike rival Honda (HMC 0.20%), which cut its profit forecast significantly on China concerns, Toyota raised its full-year profit projection, saying that its cost-cutting efforts would help offset lost ground in China.

Elsewhere in Toyota's world, the story was more positive. Strong Camry and Prius sales drove North American operating income to almost 65 billion yen, roughly double year-ago numbers -- but below analyst estimates, as margins in the U.S. market may have slipped somewhat. But Toyota's U.S. sales have been strong overall, up  30% for the year through October, with sales of the Camry sedan (up 36%) and the Prius family (up 52%) particular sources of strength.

That strength is likely to propel Toyota to the top of the global auto-sales heap for 2012. Last year's champion, General Motors (GM 1.61%), is fighting chronic problems in Europe and slipping market share in the U.S. while it overhauls its product line. That means Toyota's continued strength in Japan and resurgence here is still likely to be enough to win the crown, despite challenges in China.

The upshot: Still improving
After the troubles of recent years, Monday's earnings report was welcome news for Toyota shareholders -- notwithstanding the ongoing challenges in China. The company raised  its forecast for net income in the current fiscal year by 50 billion yen on the strength of its cost-cutting initiatives, despite a reduction in projected revenues for the period.

At this point, the post-tsunami challenges of 2011 are mostly a distant memory for Japan's largest automaker. But will it be able to overcome challenges in China -- and a resurgent GM, which will be rearmed with a slew of new products in 2013? Stay tuned.