The Audi Q5 was the brand's best-seller in the U.S in 2013. Photo: Audi.

German luxury-car maker Audi says its U.S. sales set a new record in 2013.

Audi has lagged behind its German rivals in the U.S. for years, but it has been on a tear recently. December was the 36th consecutive month in which it set a U.S. sales record, the company said in a statement on Friday. Its U.S. sales were up 13.5% in 2013.

That's good news for Audi's corporate parent, German giant Volkswagen (OTC:VWAGY). Audi is a massive source of profits for VW, and a key part of its plan to become the world's largest automaker by 2018.

So what's driving Audi's success in the U.S.? In one word or less: SUVs.

Luxury SUVs are a very profitable trend for Audi
Not all that long ago, luxury SUVs other than the horse-country favorite Range Rover were seen as an oddity. 

But now, they're seen as a massively profitable category of products. Not just in the U.S., but in China as well, where luxury SUVs have become a white-hot growth category. 

And Audi has taken full advantage. Audi is the leader of China's booming luxury-vehicle market, thanks in no small part to its SUVs. Those SUVs are playing well here in the U.S., too.

Audi says that U.S. sales of its mid-sized Q5 SUV were up over 32% in December, and up 40.8% for the full year. The large (and expensive) Q7 posted even bigger gains: Up over 52% in December, and up 45.1% for all of 2013.

But SUVs alone aren't driving Audi's success here in the U.S. More buyers are also opting for some of the brand's most profitable products: Large sedans.

Audi's big sedans are gaining ground, too
At Audi, as with most luxury-car makers, smaller sedans make up the bulk of sales. Audi's compact A4 has long been its volume leader here (though the Q5 outsold it in 2013). 

The Audi A6 sedan made big sales gains in December. Photo: Audi.

But Audi's larger cars made outsized gains in 2013. Sales of Audi's mid-sized A6 were up 43% in December, and up 18.1% for the full year. 

Audi says that sales of its higher-end models, the A6, A7, and A8 sedans and the big Q7 SUV, together made up about a third of its total sales in the U.S. in 2013. Four years ago, they represented 19% of total sales.

That's significant. It means Audi's sales mix in the U.S. is shifting toward its more profitable vehicles. That will improve Audi's profit margins -- and those margins are key to VW's global profits.

The upshot: Still well behind in the U.S., but making good progress
Audi still has a long way to go to catch up to BMW (OTC:BAMXF) and Mercedes-Benz here in the U.S. -- not to mention a resurgent Cadillac, which saw its sales rise almost 22% last year behind several strong new models.

But Audi's growth here has to be a bright sign for Volkswagen. The brand is immensely important to VW: In any given quarter, Audi's profits can make up a third to half of VW's total global earnings. (If you want to know why General Motors (NYSE:GM) has invested so much effort in its Cadillac brand, look no further than VW's quarterly earnings reports.) 

Audi's growth in China has been tremendous. But its showing in the U.S. has been underwhelming for some time. 2013's sales numbers suggest that could finally be starting to change.