After that match the Arsenal boss Arsene Wenger warned that his men could not be complacent despite their three goal advantage.
And his prediction was confirmed when Fedor Chalov and Kirill Nababkin scored for the hosts just before and after the pause.
That made it 4-3 on aggregate and another goal for CSKA would have given them the lead on the away goals rule.
As the Russians pressed for that decisive strike, Danny Welbeck reduced the deficit on the night with a right footed shot past the CSKA goalkepper Igor Akinfeev.
Aaron Ramsey netted in stoppage time to make it 6-3 on aggregate. It was a scoreline that belied the visitors' nerviness.
"Maybe we were a bit surprised by the intensity of the game and we were not at the races in the first half," Wenger told BT Sport after his side had secured a first European semi-final appearance since 2009.
"We were a bit on the ropes but we had a good response. You could see this week in Europe that you had a lot of turnarounds and you need to be completely focused."
Wenger added: "We've played against a good team. I knew that after the first game and they've shown that again. They were mobile and technically good and they gave us many problems."
CSKA coach Viktor Gancharenko praised his players for attempting to make up the three goal deficit.
"We looked very good for 75 minutes and deservedly led," he said. "We were close to a comeback but we were not close enough."