The Belgium international arrived from Everton in the summer with a £90m price tag but has done plenty to quickly justify that sum as he clinically exposed an ageing defence at the VEB Arena.
Lukaku took his tally to 10 goals in nine appearances — the great Bobby Charlton managed ‘only’ nine in his first nine — as he scored in his eighth successive European game with a double in the first half either side of an Anthony Martial penalty with Henrikh Mkhitaryan adding a fourth just after the interval.
In doing so Lukaku became the first United player to score in his opening two Champions League matches as the Red Devils established an early three-point lead at the top of Group A.
Substitute Konstantin Kuchaev’s 90th-minute goal was little consolation.
CSKA fielded three central defenders with a combined age of 101 and Viktor Vasin, the spring chicken at 28, was the only one not to be wholly embarrassed.
Manager Jose Mourinho, who made it eight wins and three draws in his own unbeaten run against Russian clubs, had warned the players he would not tolerate the sort of “PlayStation football” which had seen his side ease up at 2-0 in their opening Champions League fixture at home to Basel.
What he got was a consummate, if relatively easy, professional performance from a team missing seven senior players — including Paul Pogba, Marouane Fellaini and Antonio Valencia.
Just four minutes in Martial swung over a cross from the left to the far post where Lukaku out-jumped the 38-year-old Sergei Ignashevich to head home — making it 45 Champions League games proper without a clean sheet for Igor Akinfeev.
The goalkeeper’s legs kept out Mkhitaryan’s shot but when the Armenia international was brought down by Georgi Schennikov, Martial — a constant threat down the left — confidently stroked home the penalty.
Another Martial cross from the left was completely missed by Vasili Berezutski, 35, to present Lukaku with a simple side-foot finish to make it 3-0 and the Belgian was only denied his hat-trick by a good low Akinfeev save.
Mourinho had said pre-match the current CSKA side were the best he had faced — having been here with Real Madrid, Inter Milan and Chelsea — but that appeared flattery of the highest order.
Fedor Chalov’s 37th-minute shot brought a first-class tip-over from David de Gea but it was a rare threat from the Russian side.
Lukaku was again denied his hat-trick by Akinfeev early in the second half but when the goalkeeper parried Martial’s shot Mkhitaryan was on hand to slot home.
“That was our best first half of the season,” United defender Chris Smalling said. “We are showing that we can adapt, change formation and play in different ways. This is what we are about.”
Lukaku added: “I just work hard and will keep on going, the team is doing well but we must improve. I just want to win trophies.”
Mourinho said: “We started so strong, we surprised them with out attitude. They didn’t look as good as they are, because of us.
“Lukaku has a great record, we know he is a very good player who can score lots of goals. He is surrounded by quality players. I have to admit that he is scoring really important goals nearly every game. We are in a good position with four matches to play. We are almost there.”
Akinfeev, Vasin, Vasili Berezutski, Ignashevich, Fernandes, Dzagoev (Milanov 72), Wernbloom, Golovin, Schennikov, Chalov (Zhamaletdinov 67), Vitinho (Kuchaev 84).
de Gea, Smalling, Bailly, Lindelof, Young (Darmian 67), Ander Herrera, Matic, Blind, Mkhitaryan (Lingard 60), Lukaku, Martial (Rashford 71).
Jonas Eriksson (Sweden).