Bobby Zamora, who could be called up for England's Euro 2012 qualifiers against Bulgaria and Switzerland, opened the scoring for Fulham before going off with a knock in the second half.
Etuhu had the final word but Blackpool have now taken a heartening four points from three games in the top flight.
Varney almost put Blackpool ahead in the third minute. He tested goalkeeper David Stockdale - another possible England candidate - from the edge of the area in the third minute, the keeper reacting to see the ball to safety.
Blackpool had the ball in the net after 18 minutes but Brett Ormerod's header following a cross from Charlie Adam was ruled out for offside.
Varney was looking lively and skipped past Pantsil two minutes later, only to find the wrong side of the post with his effort.
Fulham responded and Etuhu saw his header from inside blocked after a corner by Damien Duff.
Fulham carved out a good chance in the 26th minute when Zamora worked his way into the area and tried to release Simon Davies.
But Alex Baptiste stood firm and made a crucial challenge just as his opponent was about to shoot.
Fulham made the breakthrough in the 35th minute with a simple move that split the Blackpool defence.