Ramires broke the deadlock after a neat one-two with Fernando Torres in the 26th minute as Andre Villas-Boas’ side took control of proceedings.
Raul Meireles struck the woodwork but it was David Luiz who had the best opportunity to double the lead, the Brazilian defender an unlikely penalty taker after Thomas Buffel’s handball inside the area, but his effort was saved by Laszlo Koteles.
Genk came firing out of the blocks after the break and equalised in the 61st minute when Jelle Vossen slotted home after good work from Fabien Camus.
Chelsea had chances to win the game, but Meireles headed straight at Koteles before substitute Frank Lampard spurned a glorious opportunity from close-range.
Goalkeeper Petr Cech says Chelsea will have to “do it the hard way” in their group.
“We could have put the game beyond their reach but we didn’t do and that’s why they came back into the game,” he said.
“For their comeback they deserved a point.
“We had chances to kill the game off but we didn’t do it.
“We kept organised and did what we had to do. For them it was a fantastic game and they had nothing to lose.
“When you get the opponent into this sort of mood it’s difficult.
“We could have done it the easiest way possible and play four games and be qualified so now we have to do it the hard way”.
The result was overshadowed by another racism storm for the Premier League club.
During the match, Blues fans repeatedly chanted about QPR defender Anton Ferdinand in response to the John Terry racism inquiry.
After the final whistle, a spokesperson for Chelsea said: “The chanting was wholly inappropriate and we don’t condone it.”