The Belgian striker headed home after four minutes and tapped in just before the interval for his 10th goal of the season to put the English Premier League side 3-0 ahead at halftime.
Lukaku took advantage of CSKA's porous defence, tapping in a cross by Anthony Martial that bounced past central defender Vasily Berezutsky.
Patient and energetic with the ball, United capitalised on a string of mistakes by CSKA's backline, creating space and opportunities to attack.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Martial had slotted home a penalty in between Lukaku's goals and Henrikh Mkhitaryan added a fourth in the second half to give United, three-times European champions, a maximum six points from their opening two matches.
Konstantin Kuchaev grabbed a late consolation for CSKA in the 90th minute, depriving United - unbeaten this season and level on points with Manchester City at the top of the Premier League - of a second successive Champions League shutout.
United, without first-choice central midfielders Paul Pogba, Marouane Fellaini and Michael Carrick, lead the group by three points from CSKA and Basel.
"I think a performance can only be good for the team and for the players," United manager Jose Mourinho said.
"For the team confidence is good, because six points in two matches in Champions League gives us a good position."
The absence of key midfielders was not noticeable on the pitch, and Mourinho insisted it had no impact on his team's mindset.
"It was a strong performance, a very strong start with great personality," he said.
"Nobody speaking about players that couldn't play. Nobody worries about that. Everybody is thinking in trust and belief in the players who are going to start."
Mourinho said he was pleased with United's return to the Champions League after a season out of Europe's most prestigious club competition.
"In the last appearances of Manchester United in the Champions League, the results away from home were not the best," he said.
"After one season outside, we come back and we come back in a strong way with a strong performance away."
CSKA'S defensive woes outweighed the few dangerous chances they had, including a powerful strike by Fedor Chalov that was punched over the bar by United goalkeeper David de Gea.
(Reporting by Gabrielle Tétrault-Farber, editing by Ed Osmond)
