The marathon victory was Portland's 15th triumph in 16 games. It was Chicago's second straight double overtime loss at home.
Jones hit two free throws with 12 seconds left to give the Trail Blazers a four-point advantage. He then blocked a three-point attempt by Andres Nocioni and grabbed the ball before being fouled by Joe Smith.
Two more foul shots by Jones with six seconds left clinched the game.
Brandon Roy led Portland with 25 points and Travis Outlaw had 21. The Trail Blazers have won two straight since having their 13-game winning streak halted by Utah.
Chicago's Ben Gordon scored the last two points in regulation with 67 seconds left and the game went to overtime tied at 88-88. Smith made two free throws to lift the Bulls into a 102-102 tie with 10 seconds left in the first overtime.
The Bulls were paced by 32 points from Gordon and 31 from Smith.