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With Milan and Juventus winning over the weekend, Antonio Conte's side needed three points to keep their title rivals firmly at arm's length.
It was hard work, but the points duly came their way, with centre-back Skriniar arrowing home in the 54th minute.
A rare moment of profligacy from Romelu Lukaku might have cost Inter had Duvan Zapata's subsequent effort been a foot to the right, but other than Luis Muriel's shot from a tight angle, that was the closest Atalanta came to a comeback.
Conte's temper did not take long to reach boiling point – Inter's coach receiving a caution, seemingly for complaining against the award of an Atalanta corner, in the 14th minute.
Cristian Romero almost cheered Conte up moments later when he inadvertently lobbed his own goalkeeper, with Marco Sportiello just recovering to head it over.
Samir Handanovic had to be at his best to prevent Zapata from putting Atalanta ahead before half-time, yet Inter's breakthrough came shortly into the second half, with two unlikely sources combining.
Alessandro Bastoni managed to get to a corner, and though he wanted a penalty, claiming he was pulled down, his fellow defender Skriniar was on hand to lash in.
Lukaku looked set to extend Inter's lead within four minutes, only for Romero to make a superb last-ditch challenge.
Inter's work was nearly undone with 20 minutes remaining, but Zapata dragged a low effort wide from the edge of the area.
Zapata's strike partner Muriel tried his luck shortly after, though Handanovic was again in sharp form to help Inter wrap up a 10th straight home league win.
