Watson, the Texans' first-round draft pick, completed six of eight passes for 52 yards on that drive before getting into the end zone. He showed off his mobility in the game, frequently eluding pressure to create passing lanes.
Watson did have some off-target throws, but he did a good job of throwing the ball away when there was not an open receiver.
"He's a smart player, an instinctive player," Texans coach Bill O'Brien said. "For the first game out there I thought he did some good things. That's a big jump from college to the NFL, and I thought he handled it pretty well."
"It was good just to get my feet wet," Watson said.
Watson, who led Clemson to the ACC championship on this field last December en route to winning the College Football Playoff National Championship, received a rousing ovation from Tigers fans dressed in orange when he entered the game in the second quarter.
The cheers grew louder when Watson outran two defenders for his touchdown run, although Panthers fans tried to cover the celebration with boos.
Watson looked comfortable in the pocket, stepping up to avoid pressure and getting rid of the football in a timely manner. He didn't let penalties on his team affect him and didn't turn the ball over in nearly three quarters of play.
The Associated Press contributed to this report.