Central banks from Japan, Britain and France followed the U.S. Federal Reserve in saying said they stood ready to support the global economy.
The Reserve Bank of Australia was among the first to slash interest rates on Tuesday, with Bank Negara Malaysia following close behind.
"What we needed was a reason to buy and central banks have been that reason - nothing has really changed in the coronavirus stakes from a global standpoint," said Chris Weston, head of research at brokerage Pepperstone, in a note.
Meanwhile, investors are looking ahead to a conference call, where G7 finance ministers are expected to discuss measures to deal with the economic impact of the virus outbreak, sources told Reuters.
Most Southeast Asian markets pulled back from session highs, but Indonesia and Thailand held on to their gains and ended about 3% higher.
Thai stocks surged 2.9% to post their best day since Oct. 14, 2016, as climbing oil prices boosted energy firms. [O/R]
State-run oil and gas explorers PTT Pcl gained 3.8% and PTT Exploration and Production Pcl rose 4.7%.
Indonesian shares jumped 2.9% to mark its biggest intraday gain in over four years and snap a seven-session losing streak.
The government is set to announce a second policy package aimed at reducing trade barriers as virus continues to hamper supply chains in Southeast Asia's largest economy.
Bank Central Asia Tbk PT rose 4% and heavyweight Telekomunikasi Indonesia Tbk PT gained 5.2%.
Malaysian equities rose 0.8% after its central bank cut key interest rates to a ten-year low amid a political crisis at home and coronavirus outbreak disrupting exports.
Banks helped Singapore's main index gain 0.4% after it shed nearly 5% in the past four sessions.
By Anushka Trivedi