The S&P/ASX 200 index rallied 1.2% to 6,545.00 at the close, adding to the 1% gains in the previous session.
Investors have been jittery since last week's brief inversion between the 2-year and 10-year U.S. Treasury yield curve, which has presaged several past U.S. recessions. But risk appetite recovered after China's central bank unveiled a key interest rate reform over the weekend to help steer borrowing costs lower for companies.
Earlier on Tuesday, the People's Bank of China lowered its new reference lending rate slightly, and there are expectations Beijing will take more steps to support its slowing economy, a major market for Australian firms.
Germany too has indicated it could make available up to 50 billion euros ($55.43 billion) of extra spending.
Most of the sector-based indexes in the benchmark finished in the black with the energy sector rising about 2.4% on higher oil prices.
Crude prices held on to Monday's significant gains thanks to the stimulus hopes.
Beach Energy was the top percentage gainer in the sector for a second straight session, ending 9% higher.
Shares of Oil Search gained over a percent after the firm said its half-year profit more than doubled and raised its dividend, boosted by robust output at its key Papua New Guinea liquefied natural gas project.
The Financials sub-index, an index heavyweight, closed 0.6% higher, with top lender Commonwealth Bank of Australia and No. 3 player National Australia Bank Ltd finishing 1.1% and 0.4% higher, respectively.
However, Australia and New Zealand Banking Group ended down 0.2% after it said its New Zealand arm would be most affected by the Australian regulatory decision to limit banks' exposure to their units.
Gold stocks extended falls after interests in the safe-haven metal weakened and the sub-index closed 1.3% lower.
Major gold miner Newcrest Mining Ltd ended the session down about 1%.
But BHP Group erased early losses in the session to eke out slight gains at the close. The mining behemoth's record dividend payout fell slightly short of some expectations.
Across the Tasman Sea, New Zealand's benchmark S&P/NZX 50 index gained about 1% to finish at 10,803.84.
Dairy firm a2 Milk Co was the top percentage gainers on the benchmark, closing about 4% higher.