A first-half double from Mike Magee, both from the penalty spot, had the Fire in the box seat before Dom Dwyer pulled one back for SKC with just over 20 minutes remaining, after teammate Erik Palmer-Brown was sent off.
There were a few nervy moments for the Fire but they managed to chalk up a second victory of the 2014 MLS campaign with more to come according to the boss.
"Coming away with three points against a good side is obviously the aim before the match," Yallop told reporters at Toyota Park.
"We got it done, we're unbeaten in two games, we dug through and we got the result we needed. Should have seen them off, we had a couple of chances late in the game, but we didn't take them and you've got to give credit to Kansas City.
"They kept going, created some chances late with ten men, but it's great to get that win and it felt good that we saw it through. There's room for improvement in any performance and there's no difference with this one."
Yallop added: "We're working on stuff all the time, it's brand new, we're ten games in, I'm happy with only two games lost in this league with a group that has been put together a little bit.
"Right now we're in a good spot, we've got a chance now to get going but the next four games are tough."
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