Amazon.com typically trounces Wal-Mart when it comes to online traffic on Cyber Monday, that moment after the Thanksgiving holiday when people traditionally shop from their home or work computers. But WalMart.com usually rules Thanksgiving Day, as people get ready to head out for Black Friday sales in retail stores.

That Thanksgiving pattern held true again this year -- but there are signs that it may be changing. WalMart.com was the Thanksgiving leader for the fifth year in a row, according to numbers released today by the Experian Hitwise research firm. However, Amazon narrowed the gap, grabbing 12.4 percent of the traffic received by the top 500 U.S. retail sites. Wal-Mart's traffic was just under 15 percent.

Last year, Amazon was further behind on Thanksgiving day, at 9.6 percent market share, compared with 13.7 percent for WalMart.com.

It's the latest twist in an escalating online rivalry between the companies. In recent months, the companies have been engaged in a price war that started with books but has expanded to other products and other big retail sites.

The news for Thanksgiving wasn't as good for the online economy overall: The top 500 U.S. retail sites saw traffic decline 15 percent on the day as a whole, according to the Experian Hitwise report.

In that way, Amazon was unusual in seeing significant traffic growth for Thanksgiving day. Of course, traffic doesn't necessarily translate into revenue, but it's the latest in a string of positive signs for the Seattle-based e-commerce giant, which most recently reported a big increase in its third-quarter revenue and profits.