Rubin Kazan's victory over Neftchi earlier on Thursday night meant the Italian side needed just a point in the Serbian capital to reach the knockout rounds although they were indebted to keeper Samir Handanovic for two world-class saves from Ivan Ivanov in the first half.
And Inter rewarded their keeper as Palacio netted twice and Fredy Guarin completed the triumph before Nemanja Tomic grabbed an injury-time consolation for Partizan.
The only thing left to determine in Group H will be who finishes top - which will almost certainly be decided when Kazan welcome Inter in two weeks' time.
Partizan head coach Vladimir Vermezovic still believed his side could overturn the six-point deficit the top two sides held at the start of the day - but with Rubin winning in Azerbaijan earlier, they could not afford a slip up.
They managed to subdue Inter's attacking threats in the early stages but were restricted to long-distance efforts themselves in a mundane opening.
The match sprang to life just after the half hour mark when Ivanov's bullet header was excellently tipped round the post by Handanovic.
Ivanov was sensationally thwarted again from the resulting corner, Nemanja Tomic's cross allowing the Bulgarian to power a header towards goal only to see Handanovic turn the ball away once more.
Milos Jojic squandered another chance by missing the target from close range before Palacio opened the scoring at the other end six minutes after the interval.
Guarin dribbled through two challenges on the right and his cross from the byline was chested into the net by Palacio.
Stefan Scepovic nearly drew the hosts level almost immediately afterwards but Handanovic was on hand to parry away his effort from 12 yards.
It was a pivotal stop and seemed to suck the spirit out of Partizan, who conceded a second in the 76th minute after Guarin and Palacio linked up once again.
The Argentina international, who also scored the only goal in the sides' first match two weeks ago, latched on to Guarin's through ball before slotting across Nikola Petrovic.
The Partizan keeper prevented Palacio from completing his hat-trick with a fine save but was beaten once more three minutes from time after Guarin's tap-in from substitute Antonio Cassano's left-wing delivery.
Tomic grabbed an injury-time consolation for the hosts, converting Aleksandar Miljkovic's right-wing cross, but it failed to put a dampener on Inter's celebrations.