Houston appeared to take a 1-0 lead in the 17th minute as Kofi Sarkodie got a pass in the right box and sent one across into the net, but Sarkodie was called offside.
Nielsen kept the game scoreless in the 29th minute, making a diving save to his right on Boniek Garcia's free kick from 30 yards out. The Dynamo have eliminated Kansas City from the playoffs each of the last two years.
"We knew it was going to be an ugly game, and it was," Boswell said. "But I thought we fought hard, there was no drop-off, we had guys in and out and I think everyone played well. The guys who came on gave us a boost. Like I said, you can't win it in the first game, but you can definitely lose it. And I think we've given ourselves a chance going into Kansas City."
Teal Bunbury had a shot from 10 yards out stopped in the 39th minute. On the counterattack, Will Bruin had a shot from 35 yards out in the middle sail just above the crossbar.
Nielsen stopped another Houston opportunity in the 57th minute, saving Cam Weaver's header from 8 yards out.
"Our objective wasn't necessarily to score a goal, [but] not losing, of course, and that's what we did," Kansas City midfielder Aurelien Collin said. "We could have scored a couple. I could have scored one. We didn't, but we didn't lose."
Leg 1 • Sporting K.C. 0, Houston 0
Leg 2 • Nov. 23: Houston at Sporting K.C.
Leg 1 • Sunday: Portland at RSL, 7 p.m.
Leg 2 • Nov. 24: RSL at Portland, 7 p.m.
Dec. 7 at higher seed