By Nathaniel Meyersohn, CNN Business

(CNN) -- Target capped off its best year in more than a decade with a strong holiday shopping season.

Sales at Target stores open at least a year grew 5% last year — its best performance since 2005.

Target's stellar 2018 got a big boost from the holiday season. Comparable sales grew 5.3% during its most recent quarter compared with last year. Its digital sales grew 31%.

The big-box retailer gained market share in key categories like clothes and home furnishings during the holidays and got a boost from the growing economy. Target said foot traffic to stores was up.

"We have built a successful, durable model," Target CEO Brian Cornell told investors at a meeting Tuesday. "Every piece of our strategy is working."

Target's stock rose more than 4% to around $75 a share during early trading Tuesday, despite thinner profit margins from fulfilling online orders. Target waived its minimum order requirement on online orders during the holidays.

The gap between retail's best and worst performing companies widened during the holidays and Target is among the winners. Some retailers like Target have the resources to spruce up their stores, lower prices, and speed up their online supply chains, while others struggle to stay relevant.

"As the shakeout in our industry continues, the separation between those who can afford to invest and those who can't is real," Cornell said.

The company's strategy to compete against Amazon and Walmart by focusing on Millennials and young parents with affordable brands and offering a wider array of merchandise is paying dividends.

Parents are crucial to Target's success because they spend more every year than shoppers without children.

Investments in its stores have helped, too. Target has aggressively remodeled hundreds of stores, built out delivery and buy-online-pickup-in-store capabilities, and built small stores to extend its reach within cities and college campuses.

Target also launched more than 25 exclusive brands, such as Goodfellow, a clothing label, and A New Day, a homegoods label, that burnish its trendy image. Those new brands help Target plug holes in its selection and reach different customers.

"Target's strategic initiatives announced two years ago are clearly bearing fruit, with its online push continuing to generate impressive gains," said Charlie O'Shea, analyst at Moody's.

Cornell said Target will continue to build small stores in cities and on new college campuses in 2019, as well as launch new brands. Target is also gradually expanding a free loyalty program that helps it gather key information about customers' shopping habits. The company expects sales to grow low-to-mid single digits in 2019.

Target has succeeded recently, but a parade of top retailers reported uneven results this earnings season. Some, including Walmart, TJX and Best Buy thrived. But L Brands-owned Victoria's Secret, JCPenney and Gap struggled.

Kohl's sales at stores open at least a year grew 1% during the holidays, the company announced Tuesday. Like Target, Kohl's has focused on developing exclusive brands, such as Sonoma Goods for Life and Apt. 9, to drive traffic and stand out against rivals. It has also been running a pilot with Amazon at some stores to offer free returns for customers' orders.

Under CEO Michelle Gass, Kohl's has been shrinking the size of some stores and adding more athletic brands like Under Armour to court mid-income moms. Kohl's said Tuesday that it plans to close four under-performing stores in April and open up smaller stores later this year. It can save money with small stores by carrying less inventory and employing fewer workers.

Kohl's stock rose more than 5% in early trading.