Argentine Mauro Icardi scored twice, taking his season's tally to 11, and Inter also hit the woodwork three times.
The win put them on 26 points from 10 games with eight wins and two draws, one point ahead of Napoli who visit Genoa on Wednesday. Samp are sixth after their second loss of the season.
Inter defender Milan Skriniar, who joined from Samp in the close season, got the opener in the 18th minute by scrambling the ball home from a corner and declined to celebrate.
Ivan Perisic was desperately unlucky to hit the post with a clever lob from midfield after catching goalkeeper Christian Puggioni off his line before Icardi added the second with a perfectly timed volley in the 32nd minute.
Icardi then hit the post with a header before halftime and it seemed to be all over for Sampdoria when the Argentine struck again with another volley in the 54th.
Perisic hit the bar just past the hour before Dawid Kownacki pulled one back in the 64th minute and Fabio Quagliarella then scored another for the visitors with five minutes left.
It was now panic stations for Inter as Quagliarella just missed Gian Marco Ferrari's cross and Gianluca Caprari fired over the bar before Skriniar came to the home side's rescue with a sliding tackle to stop another effort on goal.
(Writing by Brian Homewood; Editing bgy Ken Ferris)
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