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 and Lyon.
Marseille and Borussia Moenchengladbach continued their dogfight with a 2-2 draw on the French coast in Group C with on-loan QPR midfielder Barton scoring direct from a corner for the French outfit.
Russian side Rubin 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.
Bayer Leverkusen and Metalist Kharkiv 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 3-2 win over Helsingborgs 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.
They both have five points and are as many behind Fenerbahce after the Turkish champions beat Cypriots AEL Limassol 2-0 in Istanbul.
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.
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.
The result left Liverpool second, 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.
Napoli's Edinson Cavani scored four goals as the Italians twice came from behind to beat Ukraine's Dnipro Dnipropetrovsk 4-2 at home and stay in the hunt to progress from Group F.
In Group E Steaua Bucharest moved closer to qualification with a 2-1 win away to Norway's Molde for a lead of five points over Stuttgart, who beat Copenhagen 2-0 in Denmark.
Swedish club AIK beat PSV Eindhoven in Stockholm thanks to a first-half wonder goal from on-loan Celtic striker Mohamed Bangura.
Italy's Lazio beat Greece's Panathinaikos 3-0 to take a two-point lead over Tottenham Hotspur in Group J. Spurs beat Maribor 3-1 in emotional scenes as Fabrice Muamba returned as a spectator to the White Hart Lane ground where he almost died in March.
- Sports & Recreation
- Bayer Leverkusen
- Metalist Kharkiv
- Rubin Kazan