Portland rookie Greg Oden, the first pick in the 2007 draft who didn't play last season after having knee surgery, finished with 11 points and five rebounds. He picked up his fourth foul with 2:30 left in the third quarter and did not play the rest of the way.
Randolph scored 12 points in the fourth quarter to help the Trail Blazers (2-1) pull away.
Rookie Jerryd Bayless, a first-round pick out of Arizona, scored seven of his 15 points in the final quarter to give the Trail Blazers five players in double figures. LaMarcus Aldridge and Brandon Roy each added 14 points.
The Hawks (2-1) had four players in double figures with Acie Law and Josh Smith each scoring 12 points, while Joe Johnson had 11 and Flip Murray 10.
The Hawks shot only 37.7 percent from the field and missed 12 of 15 three-point attempts, while the Trail Blazers shot 58.1 percent from the floor.
The Trail Blazers (2-1) jumped out to a 15-6 lead midway through the first quarter with Oden scoring five points, including a dunk off an offensive rebound. Portland led 73-64 entering the third quarter and quickly ballooned it to 83-67 as Randolph and Bayless took over in the fourth.
Guard Rudy Fernandez, who led Portland with 15 points Wednesday in a loss to Golden State, was on the inactive list with an ankle injury. The Hawks played without Mike Bibby and Zaza Pachulia, who were both with their wives who had babies this week. They will rejoin the team Sunday for a game against Charlotte.
The game at the new Sprint Center drew 12,457 fans and was the first NBA preseason game in Kansas City since 2001.