Aleksandr Golovin put the Russian club 1-0 up on 39 minutes before Gnaly Maxwell Cornet equalised for Lyon on 58 minutes.
Musa made it 2-1 to CSKA Moscow on 60 minutes while Pontus Wernbloom scored on 65 minutes to give the Russians a 3-1 lead.
Mariano Diaz pulled a goal back for Lyon in the 71st minute which was not enough as CSKA held on to progress.
At the Emirates Stadium also on Thursday night, Arsenal defeated AC Milan 3-1 to go through to the quarter-finals of the UEFA Europa League 5-1 on aggregate.
Super Eagles forward Alex Iwobi was an unused substitute for Arsenal.
Milan took the lead in the 35th minute through Hakan Calhanoglu whose long range strike flew past David Ospina.
Arsenal were back on level terms on 39 minutes as Danny Welbeck converted from the penalty spot after he was fouled inside the box.
In the 71st minute, Arsenal went 2-1 up as Gianluigi Donnarumma parried Granit Xhaka’s low shot into his own net.
Welbeck made it 3-1 in the 86th minute, heading beyond the reach of Donnarumma who had saved Aaron Ramsey’s initial header.
The last time Arsenal progressed into the quarter-finals of UEFA competition was in 2010 in the Champions League.
And in Austria, Borussia Dortmund could only hold Salzburg to a 0-0 draw on Thursday night
Dortmund are out having lost the first leg at home 2-1 to the Austrian side.
Europa League results:
Arsenal 3 – 1 AC Milan
Olympique Lyon 2 – 3 CSKA Moscow
Salzburg 0 – 0 Borussia Dortmund