The People's Bank of China cut its one-year benchmark interest rate to 4.35% after markets had closed on Friday.
It also cut the ratio of Chinese currency it expects its banks to hold.
In reaction to the move, the Shanghai Composite closed up 0.5% at 3,429.58, while Hong Kong's Hang Seng index ended down 0.2% to 23,116.25 points.
The government is hoping that looser monetary policy will shore up economic activity to help it achieve its 7% growth target for this year.
Last week, China said its economy grew at an annual pace of 6.9% in the third quarter of the year, the weakest rate since the global financial crisis.
"The market was slightly buoyed by [China's] central bank's rate cut," said Zhang Qi, an analyst at Haitong Securities in Shanghai.
"Medium and small companies and securities companies were relatively dynamic," he said.
"But the market appeared to be in correction after it rose a lot in October, and some investors sold stocks on the short-lived rise from the rate cuts."
Shares of China Reinsurance - the country's biggest reinsurer - rose as much as 3% in its trading debut in Hong Kong. The firm's $2bn initial share sale was one of the largest in the city so far this year.
Australia's benchmark index, the S&P/ASX 200, finished the day down just 0.07% at 5,348.00, while South Korea's benchmark Kospi index closed up 0.38% at 2,048.08.
Japan's benchmark Nikkei 225 stayed in positive territory throughout the day and closed up 0.65% at 18,947.12.
Longer term
Last week, news that the European Central Bank (ECB) was considering more economic stimulus pushed shares in Asia higher.
And despite mixed trade on Monday, analysts said China's interest rate cut was likely to put further pressure on the US Federal Reserve to hold off raising rates at its meeting this week - which should boost investor sentiment globally.
"China's central bank has trumped the ECB with an actual physical move to policy - cutting the one-year lending and deposit rate by 25 basis points (bps) and slashing the reserve requirement ratio (RRR) by 50 bps," said Evan Lucas from IG Markets.
"It also added further cuts to lending rates and the RRR for certain institutions [the co-ops]," he said.
The estimated cash released from these policy changes in China is likely to be between 600bn yuan and 700bn yuan in liquidity ($93.75bn-$109.3bn; Â£61.2bn-Â£71.3bn).
"Considering [China's core inflation] reads and the industrial production reads over the past quarter, this should be no surprise," Mr Lucas said. "In fact, the surprise is that it's taken this long for the [People's Bank of China] to pull the trigger.
"What might be missed by the headline reads is that the PBoC has abolished the deposit rate ceiling - this is a big step forward in liberalising the interest rate market and shows China is very much committed to its goals of liberating the financial system," he said.
News of the world's second-largest economy, China, cutting interest rates on Friday resulted in mixed trade in the region on Monday.