The French side fell behind to a goal from Junior Moraes midway through the first half and looked in danger of being overtaken in Group F by the Ukraine side and bowing out.
But Fekir's curled shot from just inside the box meant they drew for the fifth time in the group to finish as runners-up to Premier League champions Manchester City.
Lyon had never lost against Ukrainian opposition in five previous European encounters and came into the match in good form, having lost only twice in 17 matches so far this season.
They were the better team for most of the match but suffered some hair-raising moments in the final period of the game as Shakhtar threw everything forward in search of the goal that would have taken them through.
In the end, though, it was Shakhtar's inability to keep a clean sheet -- this was their eighth European match in a row where they conceded at least one goal -- that cost them dearly.
The result means Shakhtar finish in third place and go into the Europa League knockout stage.
(Reporting by Andrew Downie; editing by Martyn Herman)
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