Target (TGT) CEO Brian Cornell came close this week to thanking Amazon (AMZN) for fundamentally changing how people shop, a profound shift the discount retailer was late in seeing coming and is still scrambling to take advantage of.

Amazon’s dominance in digital retail has been a wake-up call to brick-and-mortar retailers that shoppers will shop on their own terms, but also a revelation to those traditional retailers that their stores needn’t be albatrosses in the e-commerce era.

“We almost need to say thank you to Amazon. They have taught the American consumer to shop online, but they don’t own that relationship,” Cornell said at Re/code’s Code Conference on Wednesday.

Last quarter, Target’s online sales amounted to 2.8% of revenue, up substantially from a year earlier (2.1%) but still well below what it could have been if the retailer had been more alert to e-commerce’s ascendence. (At Walmart U.S., it’s about 4.2% of the total.)

For years, Target was focused on cultivating its cheap chic aura and landing the latest hip designer collaboration, all but ignoring e-commerce. From 2003 to 2011, Target even outsourced its web site’s platform and fulfillment operations to Amazon, unwittingly sending business to a nemesis all too happy to steal business from right under Target’s nose and leaving the company way behind many competitors.

In March, Cornell—a former PepsiCo executive and Sam’s Club CEO who came to Target last year—laid out his strategy to re-ignite growth. A key cornerstone: Spending as much on e-commerce as Target does on refurbishing and opening stores, to the tune of some $1 billion this year alone. (Please also read Fortune‘s March profile on Cornell.)

What Target and many other retailers are banking on is that e-commerce and stores can actually feed sales to another, with physical locations potentially given stores an edge over Amazon.

Cornell told Wall Street in March that a Target customer who shops both in-stores and at target.com shops three times more often that the average customer, generating three times more revenue and 2.5 times more profit. Why? Because the two avenues lead to cross-shopping and bolster customer loyalty.

Target’s strategy has been shifted to being a leader rather than a quick follower, as evidenced by its move this winter to cut its free-shipping minimum in half, from $50 to $25, squeezing its rivals. And it has also moved quickly to make sure hundreds of stores can do double-duty as distribution centers, as many Walmart and Macy’s stores do, to speed up delivery times. And Target is trying out same-day delivery with Google (GOOG) Express.

The near-crash of target.com after the Lilly Pulitzer launch in April notwithstanding, Target’s e-commerce has come along way. But Cornell wants more: He wants digital sales to grow 40% a year (it came close in the first quarter of 2015, with a 37.8% jump), something that will also help profitability as it will help reduce the pressure from shipping costs. Another thing that will help contain shipping expenses: having people come into the store to pick up an order made online.

“Our most profitable and our most valuable guest is the one who shops with us both online and in the store,” Cornell told the Re/code audience.

Target might never have known that if not for Amazon.