In a one-sided game at the San Siro, Argentine striker Milito tucked in Ricky Alvarez's cross after 13 minutes before Thiago Motta drilled in a second goal from distance.
Milito headed home Maicon's centre in the 41st minute and Giampaolo Pazzini (56) and Marco Faraoni (79) finished off Parma.
"It was important to have a good first period because Parma tend to start well with their three attackers," Inter coach Claudio Ranieri told Sky Sports.
"My players are not finished. We know we've got out of a precarious position with these five wins but we need to fly if we are going to catch those above. I'm not saying how high we can go."
Strike partner Pazzini blazed an easier chance over from another teasing Alvarez cross before the in-form Uruguayan teed up Motta to double the home team's advantage with a skidding drive.
With Inter playing on the break in the second period, Pazzini got in on the scoring act after running on to Milito's precision pass and coolly lifting the ball over goalkeeper Antonio Mirante.
An assistant referee's flag saved the blushes of Inter skipper Javier Zanetti after he belted the ball into his own net from the edge of the box before substitute Faraoni delivered a superb half-volley that crashed in off the underside of the bar.
"We allowed Inter to do too many easy things and we didn't take our chances," said Parma coach Franco Colomba after his side extended their run to six games without a win.
"We know where we need to improve. We have to find the right balance between attack and defence."
Siena, who had not scored in their five previous league matches, struck three times in the opening half through Destro's early strike and two Calaio penalties.
