A contentious goal awarded to Vitinho gave CSKA a shock lead on half-time, but Lukaku and Rashford struck twice in two second-half minutes to send Jose Mourinho's side into the last 16 as Group A winners.
After Saturday's 3-1 win at Arsenal, victory at Old Trafford sustained United's momentum ahead of Sunday's crucial derby showdown with runaway Premier League leaders Manchester City.
"I'm really happy because we don't want to qualify with a defeat, we don't want to qualify with a bad performance," said Mourinho.
"So the objective was to qualify playing well and try to get a positive result. I think we did that very, very well."
In avoiding defeat, United extended their run of unbeaten home games to 40 in all competitions, their last loss on home turf being a 2-1 defeat by City in September last year.
With Basel qualifying by winning 2-0 away to Benfica in the other group game, CSKA had to content themselves with a place in the knockout phase of the Europa League.
Mourinho made six changes to the team that had beaten Arsenal, handing a rare start to forgotten left-back Luke Shaw, and the low-key feel was only exacerbated when the Champions League music failed to play prior to kick-off.
Restored to the United attack in place of Anthony Martial, Rashford procured a couple of early chances.
He scuffed a shot against the post from Lukaku's pass and then, after Juan Mata had brilliantly brought down a lofted Daley Blind pass and cut the ball back, drew a one-handed save from Igor Akinfeev.
Making his first start since April, Shaw got forward well from his left wing-back role, stinging Akinfeev's palms with a volley and narrowly failing to pick out Rashford with a low cross.
But CSKA looked purposeful when they had opportunities to attack and after Vasili Berezutski and Vitinho had shot over, they took the lead right on half-time. And in curious fashiona.