In a clash which was billed by some as a battle for a place in the UEFA Europa League, Inter made sure it was they who impressed.
The outcome leaves them in fourth place on 47 points - that could change when Fiorentina play on Sunday - and seven clear of seventh-placed Hellas.
There was never much doubt as to who was going to be the better side after the opening minutes.
Inter started well and inside five minutes they had hit the bar as Mauro Icardo nodded Freddy Guarin's cross against the woodwork.
Home pressure continued apace and Danilo D'Ambrosio shot wide while Icardo also tried his luck with another head, this time from a Palacio cross.
Palacio would turn finisher with 14 minutes gone, though, being on the spot to tuck away Jonathan's cross after a mazy run for a deserved opener.
It was his 13th league goal of the season and did nothing to wake up the home side as Inter continued to hold court.
Luca Toni eventually stirred for the hosts and had a shot go wide, before appealing for a penalty unsuccessfully as he went down in the box.
Guarin saw a shot turned away by Rafael at the other end while Toni went off at the break complaining further about his treatment by the Inter centre-halves.
The second half saw Inter continue their first-period form, with Hernanes working Rafael and then going even closer when he thumped a free-kick against the bar.
They were desperate for the second and Guarin dragged wide after an Icardi cross, with Palacio and then Icardi himself also hitting away from goal as the frustration grew.
Jonathan was not so wasteful when he got an opportunity, though, converting from close range with 27 minutes left after smart play from Hernanes.
Raphael Martino realised Verona needed to get moving and at least made Samir Handanovic work with a shot from the edge of the box.
There would be no comeback, though, and Inter got to the finish line untroubled.