Ramires put the Blues ahead after a neat exchange with Fernando Torres before Raul Meireles hit the crossbar.
A Thomas Buffel handball gave Chelsea the chance to double their lead but David Luiz's penalty was easily saved.
The Blues were punished when Jelle Vossen scored, while Frank Lampard and Florent Malouda had chances to win it.
Lampard was guilty of an awful miss after a fine run and cross by fellow substitute Daniel Sturridge, and Malouda's effort was scrambled off the line.
The result means Chelsea will qualify for the knockout stage if they win at Bayer Leverkusen on 23 November, but anything less could see it go down to the final round of matches.
Having been shocked by QPR and Arsenal of late, the Blues arrived in Belgium wounded by what boss Andre Villas-Boas termed a "disastrous week".
The consequence was five changes to his line-up as John Terry, Lampard, Juan Mata and Sturridge dropped to the bench and John Mikel Obi missed out entirely.
Genk were thrashed 5-0 at Stamford Bridge a fortnight ago but, desperate to secure a first win in 10 attempts at this level, they looked dangerous early on.
However, Chelsea held firm and soon began to display glimpses of the attacking principles that Villas-Boas has insisted they will not relinquish despite their recent troubles.
Ramires saw a tame shot saved while Cole and Nicolas Anelka tested the Genk defence with dangerous crosses from both flanks.
The Blues were controlling possession and they duly opened the scoring, with Ramires playing a one-two with Torres before slotting underneath Laszlo Koteles.
Chelsea suddenly looked a team brimming with confidence and Torres drilled narrowly wide, Ramires headed off target and Meireles fired against the bar from 25 yards.
They were then gifted a chance to extend their advantage when Buffel blatantly handled a Malouda cross inside the box.
In the absence of Lampard, Luiz stepped up but Koteles dived to his right and comfortably saved the Brazilian's spot kick.
That gave Genk the momentum going into half-time and the hosts carried that into the second period.
Chelsea keeper Petr Cech gathered a low effort from Kevin De Bruyne - a reported Blues target - and then did even better to deflect a goalbound strike from Kennedy Nwanganga to safety.
But Genk were now stirring and it came as little surprise when they levelled.
De Bruyne fed Fabien Camus down the left and the Tunisian's cut-back was swept past Cech by Vossen with the aid of a slight deflection off Cole.
In a bid to regain control, Villas-Boas introduced Lampard and Sturridge for Ramires and Anelka and the move seemed to spark Chelsea into life.
Meireles headed straight at Koteles, Lampard fluffed his lines and a Sturridge drive was tipped over the bar.
Late on, Genk substitute Anthony Limbombe was foiled by Cech and Malouda denied by Anele Ngongca, whose goal-line clearance hit Nadson and trickled inches wide.
Genk were able to celebrate a hard-earned point, but for Chelsea it was another missed opportunity.