Amazon rose as much as 4.7 percent, putting its market capitalisation at $865.0 billion. Apple traded up 2.1 percent, giving it a market capitalisation of $864.8 billion.
Microsoft, which on Friday closed above Apple's market capitalisation for the first time in eight years, was up 0.9 percent, leaving its stock market value at $859.0 billion, third in the group.
The tight race between the trio of high-powered technology stocks coincided with a broad stock market rally after the United States and China agreed on a temporary truce in their ongoing trade dispute.
Apple in August became the first US publicly-listed company to reach a $1 trillion market capitalisation, but its share price has fallen sharply in recent months as investors worried that demand for iPhones was losing steam.
Although it is down about 13 percent from its Sept. 4 record-high close, in the year to date Amazon's stock is up 51 percent, compared to a 31 percent rise for Microsoft and Apple's 8 percent increase.