Guthrie gave up five hits, walked two and struck out three. He helped extend the Royals' scoreless-innings streak to 24, which tied a franchise record set in 1976. The streak ended in the seventh, when Ryan Madson gave up an RBI double to Brandon Phillips.
The Royals took both Interleague games against the Reds and are 26-14, the best 40-game start in franchise history.
"It's a real strong feeling that every time they walk through that door, they're gonna win this baseball game today," Yost said. "It was the same feeling we had in Atlanta for all those years. It's an attitude and a feeling that every time you walk through those clubhouse doors, you're going to win this baseball game today, and that's a great feeling."
Added Phillips, "I give credit where credit is due, and I see why the Royals made it to the World Series last year. The way they played us, that's the best team we've played all year. The Cardinals are up there, but the Royals. ... I tip my cap to those guys."
MOMENTS THAT MATTERED The Hoz show: Hosmer got things going in the second inning by rifling a double into the right-field corner. Kendrys Morales got him to third with a groundout, and Alex Gordon drove Hosmer in with a sacrifice fly. Hosmer hit a wicked grounder to second in the fourth that scored Mike Moustakas, as Hosmer reached on a fielder's choice. Hosmer then stole second and later raced home on Morales' sacrifice fly.
No slowing the Moose train: Moustakas came into the game with a team-leading .331 average. He proceeded to add three more singles, one more to left field. He also scored a run. Moustakas, with 51 hits on the season, now is hitting .342.
Moustakas continues his amazing turnaround -- last year at this time, he was being demoted to the Minors.
"I quite frankly and honestly can't say I have seen a player in the big leagues make as big an improvement as Mike Moustakas has made from last year to this year," Yost said. "And it's not even close. It's not even close. You see good players that come in, but to have to completely reinvent himself and change his game offensively, I've never seen it before."
Late at home: With runners at second and third and nobody out in the fourth, Hosmer hit a sharp grounder at second baseman Phillips, who was playing back. When Moustakas initially hesitated before taking off from third, Phillips took a couple of steps in and made a low, late throw to the first-base side of the plate. The Royals wound up with three runs in the inning and knocked out Marquis.
"He hit me with the pump fake," Phillips said of Moustakas. "If I would have thrown it right away, they all would have been safe. I have a hose, and I didn't use it that time."
Gordon crashes party: Gordon made another wall-crashing grab, this time robbing Todd Frazier to end the fifth inning. Gordon turned, raced straight back to the fence and seemed to face-plant it as he caught the ball. It was much like the catch he made to rob J.J. Hardy in the American League Championship Series against the Orioles last October at Kauffman Stadium.
"Little bit similar, just looking over the other shoulder this time," he said. "Same deal, though, and bang-bang play." More >
WHAT'S NEXT Reds: The Reds have an off-day Thursday before heading to Progressive Field for a weekend series in Cleveland. Right-hander Mike Leake will make his ninth start of the season Friday at 7:10 p.m. ET and looks to bounce back from a rough outing against the Giants. The Indians will go with right-hander Carlos Carrasco.
Royals: After an off-day Thursday, the Royals open a three-game set with cross-state rival St. Louis on Friday at Kauffman Stadium at 7:10 p.m. CT. The Royals will send right-hander Chris Young to the mound -- Young has been phenomenal in three emergency starts. Young has a career 3.65 ERA against the Cardinals.
Jeffrey Flanagan is a reporter for MLB.com. Follow him on Twitter at @jflanagankc. Robert Falkoff is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.