Inter, who beat Partizan Belgrade 3-1 in Serbia with all the goals coming in the second half, were joined in the next phase by Bayer Leverkusen, Rubin Kazan, Metalist Kharkiv, Hannover 96 and Olympique Lyon.
Russian side Kazan moved to the top of Group H, level on 10 points with Inter, after a 1-0 win at Azerbaijan's Neftchi Baku thanks to Vladimir Dyadyun's 16th minute strike.
Leverkusen and Metalist were also level on 10 points in Group K, the Germans too good for Rapid Vienna with a 3-0 home win while their Ukrainian rivals beat Norway's Rosenborg 3-1.
Palacio's double for Inter and a third from Fredy Guarin late on saw off Partizan, who netted a consolation goal in injury time through Nemanja Tomic.
Jens Hegeler's fourth-minute strike got Leverkusen off to the perfect start and goals after the break from Andre Schuerrle then Manuel Friedrich settled the outcome.
Hannover's last-gasp win came courtesy of an injury-time Szabolcs Huszti penalty that took the Germans to 10 points in Group L. Levante held Twente Enschede 0-0 in the same group and are on seven points.
Lyon maintained their perfect record with a 3-2 win at last year's finalists Athletic Bilbao to streak ahead of Group I rivals Sparta Prague, still in second after a 1-1 draw away to Israel's Hapoel Ironi Kiryat Shmona.
ATLETICO BEATEN
Wilson Eduardo netted twice for Academica against Atletico Madrid to keep alive their slim hopes of reaching the last 32 with a 2-0 win.
Czech side Viktoria Plzen took advantage of Atletico's slip-up and joined them at the top of Group B after easing to a 4-0 home win against Hapoel Tel Aviv.
Plzen and Atletico have nine points each while Academica are on four with two rounds of matches remaining in the 48-team group stage of the competition.
Treble UEFA Cup winners Liverpool suffered a setback in Moscow after they were beaten 1-0 by Anzhi Makhachkala, who went top of Group A when Ivorian Lacina Traore scored a superb winner on the stroke of half-time.
With one eye on Sunday's Premier League clash at Chelsea, Liverpool manager Brendan Rodgers fielded a makeshift side who were undone by the lanky 22-year old striker.
Traore took a long through ball into his stride and left two Liverpool defenders flat-footed with a cheeky turn before he dispatched a perfect lob over goalkeeper Brad Jones from the edge of the penalty box.
The result left Liverpool second in Group A, a point behind Anzhi on seven but level with Young Boys who were surprise 3-2 winners at Udinese. Italian striker Antonio Di Natale missed a penalty for the home side before scoring an equaliser.
Udinese are three points adrift of Anzhi.
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