The Dow Jones industrial average on Tuesday finally reclaimed the ground it held before the carnage of the Great Recession — bailouts, bank failures, layoffs by the million and a stock market panic that cut retirement savings in half.

The Dow closed above 13,000 for the first time since May 19, 2008, almost four months before the fall of the Lehman Brothers investment bank triggered the worst of the financial crisis. The closing average was 13,005.12, up 23.61 points for the day.

“People can see that the markets bounce back and are resilient over time,” said Marc Scudillo, managing officer at EisnerAmper, a financial advice company in Bridgewater, N.J. “That’s a powerful message.”

The average first pierced 13,000 last Tuesday, then floated above the milestone again on Friday and Monday, but it could not hold the mark. A 6 percent rally in the Dow this year has stalled as worries build on Wall Street about climbing prices for oil and gasoline.

On Tuesday, the Dow got the final push from a report that consumer confidence jumped in February to its highest level in a year. Improved perceptions of the job market made the difference.

The report, which came out at 10 a.m., lifted the Dow over 13,000, and it stayed there for most of the day.

“Two months ago, we were talking about a double-dip recession. Now consumer confidence is growing,” said Ryan Detrick, senior technical strategist for Schaffer’s Investment Research. “A major milestone like 13,000 wakes up a lot of investors who have missed a lot of this rally.”

The breaking of the 13,000 barrier continues a remarkable run for stocks this year. The Dow started with its best January since 1997 and has added to the gains. The index is up 6.5 percent for the young year.

Other averages have fared even better: The Standard & Poor’s 500 is up 9 percent, the Russell 2000 index of smaller stocks is up 11 percent, and the Nasdaq composite index, dominated by technology stocks, is up 14 percent.

The other major indexes sit at multi-year highs as well. The S&P closed Tuesday at its highest level since June 2008, and the Nasdaq has not traded so high since December 2000, during the bursting of the bubble in technology stocks.

Just last August, the Dow dropped 2,000 points in three frightening weeks. Investors were worried about the European debt crisis, gridlock in Washington over the federal borrowing limit, a downgrade of the U.S. credit rating and the threat of another recession.

After Labor Day, the recession fears melted away. Since then, the stock market has been engaged in a tug-of-war between optimism over the improving American economy and fear that crisis in Europe would derail the U.S. recovery.

The optimists have been winning.

The Dow cruised to 13,000 the old-fashioned way, riding the economy higher. The unemployment rate has come down five months in a row, the first time that has happened since 1994.

The economy added 243,000 jobs in January, among the three best months since 2006. Gains were surprisingly robust in industries across the economy, including the strongest hiring in manufacturing in a year.

And while the housing market remains weak, the economy did grow faster every quarter of last year.

In the stock market, the improving economy has translated to slow, steady gains — about 20 points a day for the Dow, averaged over the eight weeks. The index has gained more than 100 points on only three days, and it has not fallen 100 points on any day.

Seven of the 10 industry groups within the S&P 500 index were higher, with information technology and consumer discretionary stocks leading the way. Utility stocks, traditionally solid investments in a weak economy, were lower.

The Dow first cracked 13,000 on April 25, 2007, when the unemployment rate was 4.5 percent, far below today’s 8.3 percent, and the economy was growing at a relatively healthy clip.

From there, it was a quick ride to the Dow’s all-time high. The average crossed 14,000 in July 2007, then peaked at 14,164.53 on Oct. 9, 2007. Concerns about weak corporate earnings and tighter credit were already haunting the market, though.

The trip back down to 13,000 was less pleasant. It took little more than a month. Ten months later came the fall of Lehman Brothers investment bank and the financial meltdown. The Dow hit bottom on March 9, 2009, at 6,547.05.