Group E leaders Chelsea now have eight points from four matches, two ahead of Bayer Leverkusen who lost 3-1 at Valencia (five points). Genk are bottom with two.
"It's not a bad result away from home but we expected to win," coach Andre Villas-Boas told reporters. "We created enough opportunities to win the game but it's not happening for us in terms of efficiency.
"When you get a bad run of results you have to get a win straight away to take you out of that run," he said, referring to his team's two successive defeats in the Premier League against Arsenal and Queens Park Rangers.
Chelsea, who hammered the Belgians 5-0 at Stamford Bridge two weeks ago, showed their superior class early on and Fernando Torres chipped over the defence for Brazilian midfielder Ramires to volley in from close range in the 26th minute.
Raul Meireles then smashed a long-range shot against the crossbar in the 38th minute as the Londoners took complete control at the Cristal Arena.
A minute later Norwegian referee Svein Oddvar Moen ruled Thomas Buffel had blocked the ball in the penalty area with his raised hand.
PENALTY SAVED
David Luiz stepped forward to take the spot-kick but his weak attempt was saved by Genk keeper Laszlo Koteles diving to his right.
The home team came out fighting in the second half and received a deserved reward in the 61st minute when Fabien Camus cut the ball back for the unmarked Jelle Vossen to beat keeper Petr Cech and defender Ashley Cole on the goal-line.
Frank Lampard then missed an open goal in the closing minutes, slicing the ball wide from a metre out after good work down the right by fellow substitute Daniel Sturridge.
Florent Malouda almost snatched a winner in stoppage-time when he lifted the ball over Koteles from a narrow angle only to see the ball cleared off the line.
"Our keeper kept us in the game and in the second half we got chances and played even better than Chelsea," said Genk coach Mario Been.
Been added his side had shown Chelsea "too much respect" in the first game two weeks ago.
Chelsea and England captain John Terry, the subject of a police inquiry over alleged racist abuse against Rangers defender Anton Ferdinand, was left on the bench as Villas-Boas rotated his squad.
