First-half goals by Samir Nasri and Denilson settled the game and though the Belgians twice hit the woodwork they were second-best for most of the night.
Arsenal's victory takes them to 13 points, six clear of Olympiakos Piraeus after their goalless draw at AZ Alkmaar.
"In this group we were favourites and we just did the job," manager Arsene Wenger told a news conference.
"There are two competitions in the Champions League - one is a championship and one is a cup and now we move into the latter.
"That is much different psychologically and every minute becomes important."
Andrei Arshavin and Cesc Fabregas both shot inches wide and the match was effectively settled in first-half injury time when Denilson's 30-metre shot swerved beyond Bolat's hands.
"It was typically Brazilian, a floater, I think maybe they have shorter ankles or something that enables them to hit the ball higher on the laces," said Wenger.
Arsenal had come back from 2-0 down to win the teams' first meeting in September 3-2 but there was no sign of Liege, without key striker Milan Jovanovic, matching that, even though they had the clearer chances in the second half.
"That red card will have serious consequences for us and I'm really angry as his lack of respect for his team mates and his club," said Liege coach Laszlo Boloni.
"He has to understand the responsibility of the club is more important than his own role - I've had a word with him."
"He has big hole in his leg," Wenger said. "It doesn't look too good for him and it was a bad challenge."
