Defender Layvin Kurzawa broke the deadlock in the 73rd minute on Friday, reports Xinhua.
PSG recruited five new players this summer including Hatem Ben Arfa and Jese, trying to dominate the league again this year.
Monaco started the new season with a 2-2 draw with Guingamp, who led with 2-0 in the first half. But Monaco's Fabinho pulled one back from the penalty spot in the 70th minute and Silva scored with six minutes left.
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