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But the Champions League table-topping show was also a triumph for forgotten defender Luke Shaw who came in from the cold to remind boss Jose Mourinho he still has a future with his club.
The win also equalled a proud piece of United history, for the most consecutive home games without defeat.
United have now avoided defeat in their last 40 Old Trafford outings in the league and cup - a run dating back to the Manchester derby in September last season.
That equals the same number set by Sir Matt Busby’s United between December 1964 and March 1966.
And with City here for the eagerly-awaited derby showdown in four days, United will be aiming to set a new mark by downing Pep Guardiola’s high-flying league leaders.
But Mourinho knows they will need to be sharper in front of goal than they were last night as they needed two strikes, within 67 seconds of each other, to make sure there was no European upset.
Trailing to a shock first half opener from the visitors, Lukaku scored with a brilliant volley from eight yards from Paul Pogba’s 64th minute pass.
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And barely a minute later, the Reds were in front and heading for the last 16 as Group A winners, thanks to Rashford.
He scored an angled, left-foot shot after being played in the clear by Juan Mata’s tricky, lofted pass.
CSKA had taken a controversial lead in the 45th minute, despite weathering a half of United dominance.
Home keeper Sergio Romero’s first act in the entire game was to pick the ball out of the back of his net after Mario Fernandes’s right-wing cross was met by Brazilian Vitinho.
His strike looked to be heading into the far corner but it struck Alan Dzagoev on the back on its way into the Reds’ net.
The Reds appealed for offside but Italian referee Gianluca Rocchi quite rightly ruled that Daley Blind had been playing the visitors onside, despite having fallen off the pitch.
United needed a point to be mathematically certain of advancing to there next round - although it would have taken a catalogue of disasters for them to go out, even with a defeat.
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But Rashford was taking no chances and nearly handed United a dream start after just three minutes when he chased a Lukaku through ball and struck the foot of the post.
Minutes later, Lukaku reached the by-line and drilled over a dangerous cross which Igor Akinfeev palmed out, straight to Shaw whose shot was blocked.
Shaw was one of six changes from the impressive weekend win against Arsenal and the injury-plagued left-back was starting for the first time in over seven months.
But playing wing-back, Shaw made the most of a rare call-up and his far-post volley from Antonio Valencia’s cross drew another great save by Akinfeev who then blocked Lukaku’s follow-up.
Shaw kept up his all-star display and rolled the ball through the six-yard box for Rashford to slide in and came within inches of turning into an open net.
The shock of going behind just before the break made United all the more determined after the restart with Rashford soon stinging Akinfeev’s hands with a blast.
The excellent Shaw sent Mata away down the left for the Spanish star to cross to the far post where Chris Smalling headed tamely wide.
And Vasili Berezutski’s foul on Pogba brought a free-kick, inches outside the box, which Rashford saw deflected over via the wall.
There was a late scare when Dzagoev found himself clean through on Romero but the United deputy keeper spread himself to make a strong block.
MANCHESTER UNITED (3-4-1-2): Romero; Lindelof, Smalling, Blind; Valencia, Herrera, Pogba, Shaw; Mata; Lukaku, Rashford. Subs: Pereira, Martial, Lingard, Young, Darmian, Tuanzebe, McTominay.
CSKA MOSCOW (3-4-3): Akinfeev; Berezutski, Ignashevich, Vasin; Fernandes, Golovin, Kuchen, Nababkin; Vitinho, Chalov, Dzagoev. Subs: Pomazun, Makarov, Gordyushenko, Zhamaletdinov, Khosonov, Olanare.
Referee: Gianluca Rocchi (Italy)