The only loss came in the first of those six games, when Zack Greinke's seven shutout innings at Arizona were wasted last Friday in a 10-inning, 1-0 loss. After that, starters Luke Hochevar, Gil Meche, Kyle Davies, Brian Bannister and Greinke all notched victories.
Slowly but, they hope, surely, the Royals seem to be shaking off the effects of a 12-game skid that ended May 31.
"We've still got so far that we want to come to get out of the hole that we dug ourselves in through the losing streak," Hillman said.
"I like the way that we've been playing. Obviously, the starting pitching has been a major strength for us, but also the bullpen's picked it back up. And we've got some clutch hits and have been able to come from behind in some situations."
Before rallying to win on Wednesday at St. Louis, the Royals had been 0-37 when they trailed after seven innings.
"The starting pitching has been the stabilizer for us, but we've also seen some better at-bats," Hillman added. "We've seen [Mark] Teahen and [Alex] Gordon start to swing with a little more authority, and that helps to take some pressure off the rest of the lineup."
On the trip to Arizona and St. Louis, Teahen was 8-for-21 (.381), while Gordon went 7-for-25 (.280).
There also were seven straight games in which the starters had gone seven or more innings. That saves wear and tear on the relievers.
"Those guys are little bit more refreshed, and although we used the bullpen every day in the last series, it hasn't been overused to the point it was a couple of weeks ago, when we were going through the tough times," Hillman said.