Skriniar pounced on a loose ball from a corner to fire Inter in front nine minutes after the interval.
They had to dig in defensively late on to see out the victory, which takes them six points clear at the top.
Antonio Conte’s side have now won their past seven league games as they push for a first league title since 2010.
The defeat ended Atalanta’s own winning run, which had stood at four games, and leaves them fifth, a point and a place behind Roma.
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