NEW YORK — The Dow Jones industrial average crossed 13,000 on Tuesday for the first time since May 2008, when the Lehman Brothers investment bank was solvent, unemployment a healthy 5.4 percent and the worst of the Great Recession months ahead.

The milestone came about two hours into the trading day. The stock market got the final push from strong corporate earnings reports and a Greek bailout deal intended to prevent the next financial crisis.

The average was above 13,000 for about 30 seconds before dropping back.

The Dow last closed above 13,000 on May 19, 2008. The next day, it crossed under 13,000, not to return for almost four years. The Dow fell as low as 6,547 on March 9, 2009. It has almost doubled since then.

The 13,000 level is a psychological milepost, but in a market built on perception, it could influence more cautious investors to pump more money back into the stock market, analysts said.

“You need notches along the way to measure things, and that’s as good as any,” said John Manley, chief equity strategist for Wells Fargo’s funds group. “Is 50 older than 49 and a half? Yes, by six months. Do those six months really make a difference? Probably not. But it does give us a fixed point, something we can look at.”

Stocks dropped back slightly after hitting the mark. Just before noon EST, the Dow was up 37 points at 12,987. In other trading, the Standard & Poor’s 500 was up five points at 1,366. The Nasdaq composite index was up nine points at 2,961.

Just last summer, the Dow unburdened itself of 2,000 points in three terrifying weeks. S&P downgraded the United States credit rating, Washington was fighting over the federal borrowing limit, and the European debt crisis was raging.

The Dow fell as low as 10,655 in the fall. The 13,000 marker is a 22 percent rally from that low. The Dow is within 1,200 points of its all-time closing high — 14,164, set Oct. 9, 2007.

From here, it would take a 9 percent rally for the Dow to hit an all-time high. The S&P, a broader reading of the market, would need a bigger rally, 15 percent from here, to set a record.