Honchar, also the first Ukrainian ever to move into the overall lead, finished Saturday's 52-kilometer time trial from Saint-Grgoire to Rennes in one hour, one minute and 43 seconds.
American Floyd Landis overcame a faulty bike and finished second in the seventh stage and is now second overall by exactly one minute.
Another American, Bobby Julich, crashed on a bend and left the race with an apparent wrist injury. He suffered a similar fate in 1999, withdrawing from the race after falling in a time trial.
Germany's Sebastian Lang finished third, followed by Australian Michael Rogers, Gustav Larsson of Sweden and Germans Patrik Sinkewitz, Marcus Fothen, and Andreas Kloden.
Tom Boonen, who held the overall lead the past four days, finished 41st in the time trial and is now 21st overall.
Celebrity Families of 2014 [PHOTOS]