The blue-chip Dow Jones Industrial Average also staged a recovery, after being down most of the morning.
At close of trade it was up 82.5 points at 10,290.80.
The Nasdaq was led by rises in tech stocks like Cisco, Intel and Hewlett-Packard to close up 91.34 at 2,014.72.
But analysts were divided over whether the improvement in fortunes was just a one-day wonder.
"Whenever you have a collapse in prices like we had in the last two or three days, there are bargains and the bottom fishers come in," said Al Kugel, investment strategist at fund manager Stein, Roe & Farnham.
Japan takes hope
Japan's battered Nikkei-225 briefly traded above 12,000 on Wednesday morning, up 1.56%, but was pegged back over the session.
It ended up 23 points, just 0.20%, at 11,843. Tuesday's close was the Nikkei's lowest since January 1985.
Other Asian markets closed flat or marginally down though both Taiwan and Korea posted gains.
Slides in Europe
On Tuesday, with no clear lead from the US, European stock markets had recorded a further round of big losses, following earlier slides in Asia.
London's FTSE 100 index - which reflects the value of the largest companies listed at the stock exchange - closed 105.8 points lower at 5,720.7, levels last seen in December 1998.
In Germany, the picture was similar, with the benchmark Dax index closing 76.2 points lower at 5,970.3, while the French Cac 40 index was down 55.53 points at 5,186.87.
Earlier Tokyo's benchmark Nikkei 225 index had closed down 351 points at 11,819.7.
That means the combined value of Japan's largest 225 firms is now at its lowest level since 1985.
Nasdaq plunge
The falls earlier on Tuesday had continued the turmoil which saw America's Nasdaq stock market, dominated by companies involved in hi-tech and telecoms industries, fall below 2,000 to its lowest level since December 1998.
German DAX: 5,970.3
down 76.2
Paris Cac 40: 5,186.87
down 55.53
Nikkei 225: 11,819
down 351
Dow: 10,290.80
up 82.5
Nasdaq: 2,014.72
up 91.34
The Nasdaq lost 6% on Monday.
The Nasdaq has lost more than 60% of its value since the peak of the tech stock 'bubble' of almost exactly a year ago, when the Nasdaq composite index hit 5,048.
It also means that more than $3,000bn has been wiped off the combined value of companies listed on the Nasdaq market in the past year.
Profits warnings
This fall has not only hurt the wealth of private investors, but also the investment and pension funds of millions more.
The big falls in the US on Friday and Monday were prompted by lay-offs at computer networking giant Cisco Systems and profit warnings from Intel and Swedish telecoms equipment maker Ericsson.
Lower than expected unemployment figures in the US suggested that an interest rate cut may be likely, as traders look to that for hope in the slowing US economy.
The Japanese situation is complicated by continuing political uncertainty surrounding Prime Minister Yoshiro Mori.
US investors will be hoping for the Federal Reserve to cut interest rates again at its next scheduled meeting on 20 March.