The Comets, who won't play again until after the Olympics break, beat Minnesota, Los Angeles, Phoenix, Detroit and Chicago in the team's first five-game winning streak of the season. Houston had a four-game streak snapped at Connecticut on July 1.
Chicago's Candice Dupree made nine of her 15 shots and finished with a season-high tying 28 points. Leading scorer Jia Perkins added 15 points for Chicago (8-17), which has lost seven straight on the road.
The Sky, who beat Houston twice in 2007, have not won away from home since July 1 at Minnesota.
Chicago cut into the Comets' game-high, 15-point lead, and Dupree made a pair of free throws to make it 48-41 with 4:41 left in the third period.
But Ajavon paced the Comets with four points in a 6-2 Houston run to push the lead back to 11 with 1:56 remaining.
Perkins then hit back-to-back 3-pointers to trim the deficit to five, with 40.6 seconds to go in the third.
Houston pulled away in the fourth as Hodges and Johnson converted turnovers into back-to-back 3s with less than 5 minutes left in the game.