Leeds took an early lead, Kallum Watkins crashing over in the 11th minute after Jordan Lilley’s pass.
Liam Sutcliffe nailed the subsequent conversion to earn the Rhinos a 6-0 lead.
Charnley thought he had scored his seond try of the match just after the hour mark, but it was disallowed after confirmation from the video referee ruled there was a double movement.
Jack Higginson gave the Warriors a chance of achieving a result, crashing over in the corner after the offload from Charnley.
George Williams brought Wigan back to within two points, rounding off an excellent run and crashing over after skipping past several Leeds players.
But the Rhinos held on to record a a two-point win in a match where Frank-Paul Nu’uausala made his debut off the bench.