Yaya Sanogo scored the first goal of the game - and his first for Arsenal, after 19 appearances without a goal.
Alexis Sanchez made it 2-0 after half-time with a superb low curling shot. It's the 15th year in a row that the Gunners have made the knockout stage of the competition.
Arsenal are through to the last 16 of the Champions League after beating Borussia Dortmund 2-0 on Wednesday night, at the Emirates Stadium in London.
Liverpool were in Bulgaria to take on Ludogorets. The hosts scored in the third minute, but Liverpool's Rickie Lambert equalised five minutes later.
The 2-2 draw means that Liverpool are one win away from qualifying for the last 16.
Jordan Henderson put Liverpool ahead later on in the first half.
Liverpool were leading 2-1 until minutes before the final whistle when Ludogorets' Georgi Terziev put one in the net to equalise.
