Atalanta, whose coach Gian Piero Gasperini was infamously sacked by Inter after only five games in 2011, started the day above Inter and had been expected to provide a stern test to their opponents.
Instead, Icardi's quickfire hat-trick followed by two goals by his fellow Argentine put Inter 5-0 ahead after only 35 minutes to put a dampener on what has so far been an excellent season for Atalanta.
The win also took Inter into fourth place with 54 points, two more than their opponents who are sixth with 52. Lazio, who host Torino on Monday, are sandwiched in between on 53.
Icardi put Inter ahead in the 17th minute, scoring with his left foot from close range after Ivan Perisic's free kick deflected off the Atalanta wall and fell invitingly into his path.
After winning and converting a penalty with his right foot six minutes later, Icardi completed his hat-trick in the 26th minute by heading in from a corner.
Banega's then got in on the act as he scored twice from close range, both from Antonio Candreva crosses.
Remo Freuler pulled one back before the break but further goals from Roberto Gagliardini, who left Atalanta for Inter in January, and Banega compounded Atalanta's misery in the second half.
Napoli, who started the weekend in third place, were awarded two penalties on the way to a 3-0 win over lowly Crotone as they bounced back from their Champions League elimination by Real Madrid.
Lorenzo Insigne converted the first after 32 minutes and Dries Mertens the second, an extremely harsh decision for the faintest of touches on Marek Hamsik, in the 66th. Insigne then completed the scoring.
Napoli moved into second place on 60 points ahead of AS Roma (59) who were at Palermo later on Sunday (1945 GMT).
Nikola Kalinic scored in stoppage time to give Fiorentina a 1-0 win over Cagliari and Chievo thumped Empoli 4-0.
(Writing by Brian Homewood in Berne, editing by Pritha Sarkar)
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