SEATTLE — Olivia Zimmermann started her holiday shopping early this year, buying a Bluetooth speaker from Best Buy for her sister. It was supposed to arrive by Dec. 10, two weeks before Christmas.

The speaker never showed up — and the post office said it had delivered the package to a different town. Best Buy apologized and offered to reship it. But Ms. Zimmermann, who works in marketing in Chicago, was over it.

“I just want a refund,” she told the retailer, and then added: “At this point, I have already ordered from Amazon because I know for a fact it will be here when they say it will.”

Amazon is far and away the leader in e-commerce, outpacing competitors like Walmart, Target and eBay. But its dominance is never more pronounced than in the nail-biter last-minute sprint before Christmas.