The win, which came against one of the best pitchers in the Majors in Zack Greinke, snapped the D-backs' three-game skid as well as the Royals' four-game winning streak.
Sloppy play that culminated in a 5-0 loss here Tuesday night prompted Hinch to hold the meeting, which stretched nearly 45 minutes long as several players also spoke.
"It was a good meeting," third baseman Mark Reynolds said. "I think it brought us closer together. A lot guys aired some things out and that's what we needed. It made us a lot stronger as a group I think and it was a positive meeting and it may help down the line."
It looked like more of the same-old story in the first inning, though, as the Royals jumped out to a 1-0 lead thanks to a two-out rally against Max Scherzer.
But Scherzer (4-4) settled in and allowed just one more run before departing after six. Pitching in front of friends and family, the Missouri native got into and out of trouble for much of his time on the mound.
The Royals stranded six batters in the game's first three innings and 10 during Scherzer's six innings of work. Part of the reason for his success in keeping them off the board was that seven of the nine hits he allowed were singles.
"He seemed to get into jams and then pitch out of it," Hinch said. "[He] never really let the singles get to him. He gave up a few hits and really persevered through having guys on base. He did his part. Every time he got into trouble he got out of it. When they scored, they scored one run. He was locked in."
While Scherzer was playing the part of Houdini, the Arizona offense took advantage of two Kansas City errors in the fourth inning to score three runs and take a 4-1 lead.
Greinke (8-3) did his best to limit the damage and the Royals cut the lead to two runs heading into the top of the seventh.
With two outs and one on in the inning, Greinke faced Reynolds, who he had struck out in each of his three previous at-bats.
"It seems like against elite pitchers like that, I punch out a couple of times and then somehow find the barrel," Reynolds said.
Reynolds ran the count full before hitting a slider -- Greinke's 115th and final pitch of the night -- over the wall in left to give the D-backs a four-run cushion, 6-2.
"He's one swing away from having a great night every time," Hinch said. "I don't want to put too much on the strikeouts. He won in the long run. He can hurt you in multiple ways. Doing damage late in games after a rough couple of AB's is showing maturity."
The biggest challenge for Reynolds is keeping his focus despite struggling early in a game.
"It's real tough," Reynolds said. "You go up and you're battling your tail off to try to do something positive and he gets the best of you and it's really, really frustrating. But you've got to keep your head and just keep plugging away."
From there, the D-backs piled on against the Royals bullpen, scoring five in the eighth and one in the ninth to increase their lead to 12-2.
It was a much-needed breather for a team that has seen its share of struggles and upheaval this season. The D-backs were 12-17 under manager Bob Melvin before his dismissal and are 16-21 since Hinch took over May 8.
"Everybody got their focus back," Scherzer said of the meeting. "You play day in, day out, travel and you can lose your focus. It happens to everybody. You have a team meeting like the one we have and I think everybody got their focus back and put their focus on baseball and what comes first. I think it was evident tonight because the hitters had a tough challenge tonight and they came through and were able to score some runs off one of the best pitchers in the league."