A shopper leaves a T.J. Maxx store Feb. 21, 2007, in Framingham, Mass. Discount retail operator TJX Cos. on Tuesday said its fiscal second-quarter profit rose 31 percent as its stores like T.J. Maxx and Marshalls continued to lure in cost-conscious shoppers.

New York ? Retailers that reported their second-quarter earnings Tuesday made big strides in profitability from a year ago by slashing inventory and other costs, but executives predicted shoppers will remain tightfisted.

At discounter TJX Cos., which operates T.J. Maxx, Marshalls and HomeGoods stores, the benefit of offering low prices during the recession was clear: Profit rose 31 percent.

At Target Corp. and Home Depot Inc., profit fell but beat Wall Street expectations, while luxury merchant Saks Inc.’s second-quarter loss widened, though cutting costs helped it do better than analysts feared.

After Monday’s big sell-off, major stock indexes rose 1 percent as investors were encouraged by the better-than-expected retail earnings reports.

“Retailers have come a long way since this time last year in terms of cost-cutting, inventory management and store closures,” wrote Ken Perkins, president of retail research firm Retail Metrics, in a report released Tuesday.

Perkins now projects that, industrywide, second-quarter earnings will fall 9.4 percent, better than the 19 percent drop predicted in late March but a ninth consecutive quarter of falling profit.

Profit at Home Depot, the nation’s biggest home improvement chain, fell 7 percent during the quarter, when it shuttered its Expo Design Center stores. Excluding such one-time costs, the Atlanta-based company earned 67 cents per share, beating Wall Street’s forecast for 59 cents per share.

Home Depot earned $1.12 billion, down from $1.2 billion, or 71 cents per share, a year earlier. Blake estimated that same-store sales, a key industry metric comparing sales in stores open more than a year, will turn positive in the second half of 2010. Its revenue dropped 9 percent to $19.07 billion.

Home Depot raised its full-year guidance, and its shares rose 82 cents, or 3.1 percent, to close Tuesday at $26.93.

Chairman and CEO Frank Blake said Home Depot took market share from competitors, but he said same-store sales fell in most regions.

“We remain concerned by the high level of foreclosure activity, which we believe continues to put pressure on the housing markets in those areas, as reflected in lower sales of basic building material products,” he said.

Declining crude oil prices, which lowered transportation costs, combined with cost cuts to help Minneapolis-based Target earn $594 million, or 79 cents per share, in the quarter. That compares with $634 million, or 82 cents per share, a year earlier and with an average analyst forecast of 66 cents per share on revenue of $15.1 million, according to Thomson Reuters.

Revenue fell 2.6 percent to $15.07 billion.

Its shares rose $3.11, or 7.6 percent, to close Tuesday at $43.32.

Many discounters, particularly Wal-Mart Stores Inc., have benefited from consumers switching to cheaper stores and focusing on necessities. But at Target, where more than 40 percent of revenue comes from nonessentials like funky jeans and bedspreads, the cheap-chic formula has became a drag.

TJX — whose stores including TJ Maxx, HomeGoods and Marshalls are attracting consumers seeking cheaper clothing and other products — rose 31 percent to $261.6 million, or 61 cents per share, beating Wall Street’s expectations by 1 cent. Revenue rose 4 percent to $4.75 billion, meeting analyst estimates, and TJX’s same-store sales rose 4 percent.

Its shares fell $1.05, or 3 percent, to close Tuesday at $34.33.

Saks’s results offered a clear contrast. It lost $54.5 million, or 39 cents per share, compared with a loss of $32.7 million, or 24 cents per share, a year earlier. Analysts forecast a loss of 52 cents per share on revenue of $563 million.