So naturally, this time Alexander gave up a double and a single, and suddenly the White Sox had runners on first and third with none out.
No problem. Alexander had them right where he wanted them. He struck out Yoan Moncada, got Jose Abreu to pop out and then induced a groundout by pinch-hitter Matt Davidson to secure a harrowing escape and a much-needed Royals win.
What was Alexander's mindset?
"Just trying to get outs any way I can," Alexander said. "That situation, everyone playing great, you don't want to be the one to blow it. Just keep that run from scoring, or at least not give up the lead."
The key out was the strikeout of Moncada. Kansas City manager Ned Yost had the infield at three-quarters depth in an attempt to cut off the potential tying run on a grounder.
But Alexander instead threw three heavy sinkers past Moncada for out No. 1.
"That was huge, just obviously to get an out and get some momentum going," Alexander said. "Now maybe we can get a ground-ball double play. Definitely took some pressure off. Actually, I'm not even thinking strikeout there. Just want some weak contact and get an out."
Next came the dangerous Abreu. Alexander, a ground-ball pitcher, still isn't sure how he got him to pop out.
"I don't know," Alexander said. "I lost it. I didn't even see it. I'll have to go back and look at it."
And then Alexander got Davidson to ground out to third, and the Royals breathed a collective sigh of relief.
"I just wanted to come in and do the best I can to help us win. Just want to do my part," Alexander said. "Just thinking [about the] task at hand."
Jeffrey Flanagan has covered the Royals since 1991, and for MLB.com since 2015. Follow him on Twitter @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.