Osweiler, who signed to a $72 million contract from Denver in the offseason, was helped by an offense filled with playmakers.
"There was nothing about the game that was perfect but we just kept playing ... and we made the big plays when we needed to," Osweiler said.
He completed passes to eight different receivers, led by rookie first-round pick Will Fuller, who became the first player in franchise history to have 100 yards receiving in a debut with 107 and a touchdown. DeAndre Hopkins added 54 yards and a score and running back Lamar Miller had 106 yards rushing in his first game with the Texans.
Osweiler's day started with a hiccup when he threw an interception on the first drive, but soon got going and looked comfortable after that.
Houston trailed by 1 point entering the fourth quarter before Osweiler found Fuller on a short pass and he scampered 18 yards for a touchdown to make it 20-14.
"Those struggles occurred a little bit more in the second half when we had to play backyard football where we had to throw it to catch up," Chicago coach John Fox said. "They're a talented front and when you get too one-dimensional like that, it becomes problematic for everyone."
Copyright 2016 by The Associated Press