Fehr scored the first and fourth goals for the Capitals. His tiebreaking goal -- at 5:02 of the third period -- came when he took a pass from Mathieu Perreault and beat Mathieu Garon. Fehr's first goal made it 1-0 at 6:29 of the first period.
Ovechkin, playing his second game of the preseason, and Green had assists on a goal from Backstrom that gave Washington a 3-2 lead 71 seconds into the third period.
Ovechkin, who added another assist on a last-minute empty-net goal by Semin, was involved in a third-period skirmish with Columbus' Nick Holden and sent off the ice for a 4-minute roughing penalty.
The Blue Jackets' Mike Blunden was called for a 4-minute high-sticking penalty just 13 seconds into the second period and Laich gave Washington a 2-0 lead 10 seconds later.
Wilson's short-handed goal cut Washington's lead to 2-1, and Holden's score tied the game at 2 at 14:03 of the second.
After Backstrom's backhanded flip gave the Capitals a 3-2 lead early in the third, Clark tied the score at 4:12.
The Capitals will try to complete their perfect preseason on Sunday against Nashville. They've outscored their opponents 20-9.
Columbus' preseason will end with a hectic few days. This was the second of back-to-back-to back games. The Blue Jackets beat the Wild 4-2 at Minnesota on Thursday night and will host Atlanta on Saturday before flying to Sweden for a game with the Malmo Redhawks on Tuesday.
Copyright by STATS LLC and The Associated Press
Arena: Verizon Center Location: Washington, District of Columbia
Referees: Fred L'Ecuyer, Paul Devorski Linesmen: Brian Murphy, Derek Nansen
Attendance: 17,496 (95.1% full)
Eric Fehr 1 Assist: Mike Green, Marcus Johansson
Brooks Laich 1 (power play) Assist: Eric Fehr
Kyle Wilson 2 (shorthanded) Assist: Chris Clark
Nick Holden 2 (power play) Assist: David Savard, Michael Blunden
Nicklas Backstrom 3 Assist: Alex Ovechkin, Mike Green
Eric Fehr 2 Assist: Mathieu Perreault
Chris Clark 1 (power play) Assist: Rostislav Klesla, Derek MacKenzie
Alexander Semin 2 (empty net) Assist: Alex Ovechkin