The days of big-box retail dominating the market place are over. Brick-and-mortar stores that want to compete have to have everything online that compliments their traditional store presence, whether it is free-standing or in a mall. E-commerce sales rose to 10.5% of total retail sales in the fourth quarter of 2013 (total retail sales excluding auto dealers and food and beverage stores), setting a record high penetration, as it has every fourth quarter for more than a decade. The top retail names that embrace e-commerce are prepared to win the war, not just the battle.

In a new research report, the retail team at Stifel did an outstanding job of finding which traditional retailers had actually matched every metric in their omni-channel scoreboard. Five top names did extremely well in categories that range from having a website to providing a mobile app and customers being able to check store inventory online. Given the competition these days for consumer dollars, these may very well be the only five to own.

Autozone Inc. (NYSE: AZO) has become the retail stock that momentum traders have fallen in love with. With Americans having the oldest average car age in almost two decades, it may stay strong. This year’s unusually cold winter has been a source of frustration for drivers, but it has been a boon for car maintenance specialists and auto parts dealers. Cold weather and icy roads means more accidents and more car parts failing. Just what the doctor ordered for Autozone. The Stifel price target for the stock is set at $570. The Thomson/First Call estimate is at $528.06. Autozone closed Tuesday at $539.30.

Best Buy Co. Inc. (NYSE: BBY) has been absolutely destroyed since announcing weak holiday sales numbers and poor follow-up numbers in January. The company has met its rivals head-on with price-matching policies that largely eliminated the advantages of its competitors. More importantly, its store-within-store formats for makers of popular mobile devices and computers have drawn interest from major manufacturers, letting Best Buy take advantage of its retail space to give it competitive advantages that online retailers cannot match. Investors are paid a 2.8% dividend. The Stifel price target is $30, and the consensus target is $33.86. Best Buy closed Tuesday at $25.31.

O’Reilly Automotive Inc. (NASDAQ: ORLY) has ridden the same positive wave that Autozone has. In fact, the current growth estimate for this year calls for earnings per share to rise 16.3%. Furthermore, the long-term growth rate is currently an impressive 15.6%, suggesting pretty good prospects for the long haul. The Stifel price target is $145, and the consensus is posted at $154.42. The stock closed Thursday at $153.34. It seems likely the Stifel target is raised.

Sotheby’s (NYSE: BID) has ridden a huge move up in artwork and posted incredible earnings. Hedge Fund manager Daniel Loeb’s fourth largest holding is in Sotheby’s, where the guru maintains 6,350,000 shares of the company’s stock. His position makes up for 5.8% of his total portfolio and 9.29% of the company’s shares outstanding. Investors are paid a small 0.8% dividend. Stifel has a $65 price target, and the consensus target is $52.80. Sotheby’s closed Tuesday at $48.75.

Tiffany & Co. (NYSE: TIF) has seen consistent floor traffic and sales from its base high-end clientele. The company’s jewelry products include fine and solitaire jewelry; diamond engagement rings and wedding bands to brides and grooms; and non-gemstone, sterling silver, gold, metal and platinum jewelry. The company also sells timepieces, leather goods, sterling silver goods, china, crystal, stationery, fragrances and accessories. Above all, Tiffany is one of the most highly regarded luxury retail names in the world. Investors are paid a 1.5% dividend. The Stifel price objective is $92, while the consensus target is $96.14. The stock closed Tuesday at $90.77.

Online shopping is becoming easier and more convenient, while consumers are becoming more comfortable with online and mobile shopping. Retailers looking to participate in e-commerce growth must participate via mobile. These top five stocks to buy have all scored very well on the Stifel omni-channel scoreboard and may prove to be excellent portfolio additions.

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