Celtic gave their chances of reaching the last 32 a boost by beating Ferencvaros 3-2 in Hungary, while Rangers also have it all to play for in the final two games after coming from behind to draw 1-1 away to Brondby.
West Ham are on the brink of guaranteeing top spot in Group H which will book their place in the last 16, but needed Said Benrahma to score twice in Belgium to preserve their unbeaten record in Europe.
In the 1 000th game of his managerial career, David Moyes took the opportunity to rest a number of his key players ahead of Liverpool's visit to the London Stadium on Sunday and paid the price with a slow start as Joseph Paintsil opened the scoring for Genk after just four minutes.
The introduction of Soucek, Pablo Fornals and Jarrod Bowen after the break helped turn the game around.
Benrahma rounded off a brilliant team move to equalise before using his individual skill to wriggle free of the Genk defence and fire powerfully in at the near post.
However, the visitors dropped points for the first time in the group when Soucek's diving header flew into his own net three minutes from time.
"It's a moment I'll really remember because the game will always be remembered for Tomas Soucek's own goal!" Moyes said on his personal landmark.
"But overall I am thrilled to reach a thousand games. It is a great achievement."
LEICESTER PAY PENALTY
Leicester remain third in Group C after Jamie Vardy missed a second-half penalty at the King Power.
Victor Moses headed the Russians in front before Daniel Amartey quickly levelled.
Vardy's spot-kick was saved by Aleksandr Selikhov with 15 minutes remaining.
Serie A leaders Napoli now top the group after thrashing Legia Warsaw 4-1 to move onto seven points with the Poles on six and Leicester on five.
Celtic closed to within a point of Real Betis in Group G thanks to goals from Kyogo Furuhashi, Jota and Liel Abada in Budapest.
Betis were thrashed 4-0 by Leverkusen with Moussa Diaby scoring twice for the Germans.
Leverkusen need just one point from their remaining two games to guarantee top spot and a place in the last 16.
Lyon are already into the last 16 as a 3-0 win over Sparta Prague won Group A.
Sparta and Rangers are level on four points, but the Czechs have the advantage on head-to-head record ahead of the meeting between the sides at Ibrox on November 25.
Ianis Hagi came off the bench to salvage a point for the Scottish champions in Copenhagen after they fell behind to Leon Balogun's own goal.
A four-goal thriller that ended 2-2 between Marseille and Lazio left Group E as it was at the start of the evening as Galatasaray were held 1-1 by Lokomotiv Moscow.
The Turkish giants lead the section on eight points, three clear of Lazio with Marseille one further back.
Monaco maintain a two-point lead over LaLiga leaders Real Sociedad after both games in Group B ended in draws.
Sociedad could only manage a 1-1 draw at home to Sturm Graz to give PSV Eindhoven hope of qualifying as they drew 0-0 in the Principality. (AFP)

Khan warns Paul ahead ‘life-threatening’ Joshua fight
Emery's perseverance & belief key to Villa resurgence
Agu backs Okoye for Eagles No. 1 spot
PFL contract ends soon - Ngannou
'No-one downing tools' - Alonso's stay of execution despite loss to Man City
Zaha in Ivory Coast Afcon squad but Adingra left out
UCL: Mbappé doubtful for Manchester City clash after missing training
'Give Alonso time' - but Man City visit could be pivotal
Fifa accused of breaching own rules with Trump award
Son, Simons and mini Spurs revival lift Frank's spirits
Finidi challenges Rivers United players’ mentality
Rangers International going, going . . . (63,402 views)
Amaju Pinnick: A cat with nine lives (54,646 views)
Second Term: Amaju Pinnick, Other NFF Heavyweights Home to Roost •How Pinnick Broke the Jinx (52,587 views)
Current issues in Nigerian sports: Matters arising (52,220 views)
Sports Development: Zenith Bank on the zenith (52,194 views)
Missing $150,000 IAAF Grant: Solomon Dalung’s Hide and Seek game (52,105 views)
Gov. Abdullahi Ganduje’s solid footprints, commitment to sports development in Kano State (51,950 views)
NFF Presidency: Pinnick, Maigari, Ogunjobi, Okoye in Battle for Supremacy (51,535 views)
Olopade, BET9A wave of revolution in NNL (50,676 views)
Commonwealth Games 2018: Shame of Muhammadu Buhari, Solomon Dalung (49,224 views)
Ibrahimovic’s Man U exit: Whose decision is it? And in whose interest? (47,618 views)
John Mikel Obi: Segun Odegbami’s Outrageous Call! (47,090 views)