Kyle Wilson and Chris Clark each had a goal and assist for Washington, 2-0-0 in exhibition play.
Wilson ripped in a low shot from the slot to tie the game at 2 with 2:47 left in the third period to set up overtime.
Washington rookie Michal Neuvirth stopped 24 shots.
Chicago's lineup was made up mostly of regulars from last season, when the Blackhawks had 104 points and reached the Western Conference finals. The Capitals' lineup included mostly younger players and prospects.
Washington left wing Alex Ovechkin, the NHL's goal-scoring leader last season with 56, was a healthy scratch for the second straight game.
Sharp opened the scoring 4:52 in on a rebound of Dustin Byfuglien's shot. Skille gave Chicago a 2-0 lead at 5:54 of the second on a rising, screened shot from right wing.
Clark cut it to 2-1 midway through the second, when his centering pass intended for Wilson deflected in off the skate of Chicago defenseman Brent Seabrook.
A Blackhawks' preseason record 19,734 fans a sellout attended the game in the newly reconfigured United Center.
Chicago center Dave Bolland remains out with a lower-back injury. ... Washington right wings Eric Fehr and Tomas Fleischmann have undisclosed injuries. All three were regulars for their teams last season.