Diego Milito scored twice and Thiago Motta was also on target as Inter laid the foundations for victory with one of their best halves of the season.
Giampaolo Pazzini and Marco Faraoni struck after the break to seal an impressive win which sends the Nerazzurri to within three points of the top three ahead of Sunday's remaining fixtures.
Milito was the hosts' main threat in the penalty area, but the architect of the performance was Ricardo Alvarez.
From the moment he dragged the ball past a defender with the studs of his boot with his first touch he appeared to have a new air of confidence about him, and it did not take long for him to create the opening goal.
His perfect cross to the near post was guided home with the outside of his right boot by Milito.
In the 18th minute, Milito's shot was blocked and the ball fell out to Motta, whose volley from 20 yards flew past Antonio Mirante to make it 2-0.
Sebastian Giovinco was Parma's only threat and his header wide in the 20th minute was followed by two trademark free-kicks which Julio Cesar had to be alert to keep out.
Inter's third came in the 41st minute with Maicon lifting the ball into the area for Milito to head in unchallenged from eight yards for his sixth goal of the season.
There was no let-up from Inter in the second half and Pazzini made it four 10 minutes in when he latched on to Milito's pass, despite a hint of offside, and lifted the ball over the onrushing Mirante.
It was clearly not Parma's night as they had a goal disallowed when Javier Zanetti put through his own net, but the offside flag was raised against the nearest Parma striker.
Five minutes later, Inter substitute Faraoni sealed the win with a dipping shot from 20 yards out which grazed the underside of the crossbar on its way in.
Alvarez and Milito both left the field as boss Claudio Ranieri withdrew the pair in the final 10 minutes, affording them a standing ovation, as Inter got their title challenge back on track.