A surge in online shopping and higher spending by low-income Americans gave a lift to the start of the holiday season, even as initial reports showed that foot traffic to traditional stores continued its long decline.

During Thanksgiving and Black Friday, traffic to U.S. stores fell between 5% and 9% compared with the same days last year, estimated RetailNext, which uses cameras to track people in both mall-based and stand-alone retailers. Another measurement firm, ShopperTrak, estimated traffic fell less sharply, about 1%...