Antoine Kombouare's men headed into Friday's game at the Stade de la Licorne in Amiens – serving as their main home stadium while them Stade Felix Bollaert undergoes renovation for Euro 2016 – having claimed just four league wins in a season marred by financial troubles.
But they secured their fifth triumph with a strong performance to lift them above Bastia and Metz and further tighten matters at the wrong end of the French top flight.
Cyprien opened the scoring in the 38th minute as the midfielder curled Lalaina Nomenjanahary's pull back beyond Simon Pouplin following good work down the left from the Madagascar forward.
The 19-year-old Cyprien was involved again as Lens were handed a golden chance to double their lead.
France Under-19 international Cyprien was felled by Souleymane Diawara in the area, however, Coulibaly sent the resulting penalty kick sailing over the crossbar.
Coulibaly atoned for that error four minutes from time, though, cleverly cutting in from the left beyond two defenders and coolly slotting home at the near post to wrap up the points and boost hopes that Lens can avoid the drop when the campaign resumes in the new year.