Palacio nodded home from a Diego Milito cross less than a minute after Lazar Markovic had a shot saved by Samir Handanovic at the other end, sending Inter joint top of Group H on seven points.
Inter share their lead with Rubin Kazan, for whom Alan Kasaev's 16th-minute goal proved enough to see off Azerbaijan side Neftci in Russia. Inter and Kazan now hold a six-point advantage over their group rivals.
Elyaniv Barda also headed a late winner as Genk stayed unbeaten at the top of Group G after coming from behind to see off Sporting Lisbon 2-1 in Belgium.
Stijn Schaars put Sporting ahead on eight minutes, but Benjamin De Ceulaer equalised after 25 and Barda struck with three minutes to go after Sporting's Khalid Boulahrouz was sent off for a second bookable offence.
And Hungarians Videoton also continued their excellent form in the group with a 2-1 win over Basel. A Fabien Schar own goal paved the way for the hosts, who extended their lead through Marco Caneira before Schar scored at the right end in injury time.
Lyon maintained their 100 per cent record in Group I with a 2-1 win over last year's beaten finalists Athletic Bilbao.
A Lisandro Lopez opener was cancelled out by Ibai Gomez before Jimmy Briand struck the winner four minutes from time.
First-half goals from Ladislav Krejci, Vaclav Kadlec and Ondrej Svejdik helped Sparta Prague to a 3-1 win over Ironi Kiryat Shmona, for whom Shimon Abuhatzira replied late on.
Lyon lead the group on nine points with Sparta clear in second on six.
Substitute Jose Toche grabbed an injury time equaliser as Panathinaikos drew 1-1 with Lazio in Group J. An own goal from Giourkas Seitaridis looked set to give the Italians the points before the late drama.
Gylfi Sigurdsson earned Tottenham a point in a 1-1 draw at Maribor, who led through Robert Beric.
Lazio remain unbeaten on five points with Maribor in second, but all four sides are still in the running.
Late goals from Bonfim Marlos and Cleiton Xavier gave Ukrainians Metalist a 2-1 win at Rosenborg in Group K, after the Norwegians had led through Tarik Elyounoussi's 46th-minute strike.
But Metalist still conceded top spot in the group to Bayer Leverkusen, whose crushing 4-0 win at Rapid Vienna took them first on goal difference. Philipp Wollscheid, Karim Bellarabi and two from Gonzalo Castro did the damage.
In Group L, Hannover stayed top after a dramatic 2-1 win at Helsingborg, Mame Biram Diouf opening the scoring for the Germans with Alvaro Santos equalising in injury time, only for Didier Ya Konan to restore Hannover's advantage in the third minute of added time.
Levante moved clear in second place with a 3-0 win over Twente, a Michel penalty setting them on their way and Pedro Rios adding a late double.
Reigning champions Atletico Madrid maintained their 100 per cent record in Group B with a 2-1 win over Academica, Diego Costa and Emre Belozoglu netting before Salim Cisse hit a late consolation for the Portuguese side.
Also in Group B, Viktoria Plzen moved clear in second place with a 2-1 win at Hapoel Tel Aviv.
Hanan Maman put the Israelis in front after 19 minutes, but Pavel Horvath equalised in first-half injury time and Frantisek Rajtoral hit the winner before home defender I'yad Hutba was sent off.
In Group A, Liverpool grabbed a potentially crucial 1-0 win over big-spending Russians Anzhi Makhachkala at Anfield, with Stewart Downing drilling the only goal after cutting in from the left after 53 minutes.
Their win helped Brendan Rodgers' men jump two places to lead the group after a shock 3-1 defeat for Udinese away to bottom side Young Boys in Switzerland.
Raul Bobadilla grabbed a stunning hat-trick for Young Boys, who had gone into the game without a point, putting them 2-0 up with goals in the fourth and 72nd minutes and then wrapping up victory with a penalty after Andrea Coda briefly reduced the deficit.
It was also all-change in Group C, where Egeman Korkmaz scored in the 72nd minute to give Fenerbahce a 1-0 win at AEL Limassol and move them to top the top of the group.
Marseille, who started the night on top, lost 2-0 at Borussia Monchengladbach, a Filip Daems penalty and a second-half strike from Peniel Mlapa moving the Germans level with their opponents on four points, with the Turkish side now out in front on seven.
Newcastle strengthened their hold on Group D, Gabriel Obertan giving them a 1-0 win over Club Brugge, while second-placed Bordeaux were held 1-1 at Maritimo.
Yoan Gouffran's opener for the visitors was cancelled out by Roberge Valentin six minutes later.
Steaua Bucharest extended their lead at the top of Group E as goals from Vlad Chiriches and Raul Rusescu gave them a 2-0 win over Molde, while group rivals Stuttgart and FC Copenhagen played out a goalless draw in Germany.
Dnipro went five points clear at the top of Group F with an excellent 3-1 win over Napoli in Ukraine, Artem Fedetskiy, Matheus and Giuliano scoring before Edinson Cavani replied with a late consolation.
PSV Eindhoven and AIK drew 1-1 in Holland, Kwame Karikari putting the previously pointless Swedes in front on the hour before Jeremain Lens equalised with 10 minutes to go.
Europa League Results