Norris sent down nine of the 10 batters he faced, allowing only a one-out walk in the first inning. Harrell, a candidate to win a long-relief spot in the bullpen, threw three perfect innings in relief and struck out a pair of batters.
Astros manager Brad Mills said Norris was held to three innings because he felt tightness in his triceps prior to the game, but it's not a concern.
"I wanted to get three or four innings of work and get to the pitch count," Norris said. "It was predetermined, so I went out there and did that. I was a lot better mechanically, and that's why you have spring starts -- to get more comfortable."
The Nationals didn't manage a hit until Jayson Werth rolled a single up the middle with two outs in the seventh off former Phillies teammate Brett Myers, who threw his fifth consecutive scoreless outing. Former Astro Jason Michaels got Washington on the board with a solo homer in the eighth inning.
Up next: The Nationals go to Sarasota, Fla., to play the Orioles at 1:05 p.m. ET on Saturday. Edwin Jackson will get the start for Washington. In his last start, Jackson pitched four innings and allowed four runs on seven hits against the Tigers. It will be also a homecoming for shortstop Ian Desmond, who was born and raised in Sarasota.