Bargain-hunters drove Tokyo to another seven-month high. Tokyo's Nikkei 225 average shook off early profit-takers to gain 1.22 percent to 16,268.11 as overseas investors hunted bargains in the shade of the Dow's towering rise.
Hong Kong's Hang Seng Index made another bull run at the 11,000 mark, but ran out of energy to end 0.26 percent up at 10,940.07, a 1999 high.
Analysts said the market was running into profit-taking and uncertainty around 11,000, especially in light of Wall Street's failure to sustain the 10,000 mark.
Australia's All Ordinaries ran out of steam after three straight days of record highs, dropping 0.48 percent to 2,977.8.
"We have taken it a bit easier today. Some are using the Dow as an excuse, but plenty of these stocks have run hard and people now think it is sensible to take some profits," said a Sydney-based trader.
The Taiwan Weighted rose 1.27 percent to 6,757.07, but Singapore fell back, ending 1.3 percent down at 1,470.16.
South Korea started strongly, rising on Wall Street's strength, but profit-takers punctured the mood later in the day, with the index ending down 0.22 percent at 600.52.
Wall Street gave another boost to Jakarta, with dual-listed stocks again lifting the index. The JSX index ended 2.22 percent up at 387.881.
With a running start, it took all of 20 minutes for the Dow to rush to the brink of 10,000 Tuesday morning, reports CBS News Correspondent Anthony Mason.
At the New York Stock Exchange, traders stopped, stared up at the board and erupted as the Dow broke five digits for the first time ever.
But the celebration on the trading floor didn't last long. It couldn't. The Dow ran out of gas almost as soon as it crossed the mark. It only took a couple of minutes to slip back below 10,000.
The Dow rose as high as 10,001.78 before losing steam. It finished the day 28.03 points lower at 9,930.74.
Still, it was a milestone.
Veteran trader Jay Duryea was impressed: "Five years ago to this day the market was at 3888... It's an extraordinary event."
But to Wall Street legend Ace Greenberg, it was just another number. "No celebration. I'm not buying drinks for anybody. Not even me."
Does it count until it closes at 10,000? "Not as much," says Duryea.
After four days of flirting, the market was left with the memory of a fleeting kiss.
The average of 30 blue-chip stocks took almost a year to gain the final 1,000 points in its charge after passing 9,000 on April 6, 1998. The 1990s bull market was all but written off last summer and early autumn as it plummeted after Russia's economic crisis, only to rebound on a series of three interest rate cuts by the Federal Reserve.
Wall Street's best-known indicator has been pumped up by its own momentum, including a spurt of more than 700 points in the pastwo weeks. By reaching five digits, the Dow is now up nearly 9 percent this year on top of an unprecedented four straight years of double-digit growth.