Kansas City Police Dept. -- CRIME DOWN ... During Royals Playoff Game

The Kansas City Royals could be the key to stopping crime in Kansas City ... because criminal activity was actually DOWN in K.C. during last night's big playoff game ... cops tell TMZ Sports.

We spoke with Sgt. Darin Snapp of the Kansas City Police Dept. who says the unbelievable 12 inning battle between the Royals and the Oakland A's may have actually deterred the bad guys for a night.

"We ran the last 4 Tuesdays and last night was the slowest night as far as calls to service," Sgt. Snapp says ... adding, "Everybody was happy and getting along and watching the game."

The cops were especially thrilled with the situation ... considering the KCPD had tweeted out to the city earlier, "We really need everyone to not commit crimes and drive safely right now. We'd like to hear the @Royals clinch this."