Kennedy pitched four-hit ball for seven innings, Morales hit a three-run homer and drove in four runs, and Kansas City blanked the Cleveland Indians 7-0.
"That's just what the doctor ordered," Royals manager Ned Yost said. "A really good pitching performance by Ian. Kendrys took some pressure off him and he took it from there."
Kennedy (4-2) worked out of a bases-loaded jam in the sixth and retired 14 in a row at one point. He struck out six while helping end Cleveland's four-game winning streak.
"That's a good lineup," Kennedy said. "I had to constantly throw everything for strikes and mix it up."
Morales' homer in the first provided an early boost for Kansas City's struggling offense. He added an RBI single in the eighth.
Kansas City's win came at an opportune time. The Royals had lost eight of 10 and announced before the game that third baseman Mike Moustakas was put on the 15-day disabled list with a fractured left thumb.
The World Series champions had scored 21 runs and been shut out three times in 10 games going into Saturday, but that problem was quickly resolved.
"The last week, it seems like every time we play the first inning we're down two or three runs," Yost said. "To be up three runs for the first time in awhile, it's big."
Anderson (0-2), called up from the minors before the game, allowed four runs in five innings.
Kennedy gave up two hits in the first. Cleveland didn't have another baserunner until Juan Uribe's leadoff single in the sixth. The Indians loaded the bases with two out, but Carlos Santana grounded out.
"It's nice when the boys score some runs for you and get you on the board early," Kennedy said. "The last thing I want to do is give up some runs after that."
"He just pitched really well," Indians manager Terry Francona said. "He threw a lot of strikes and didn't put the ball over the middle of the plate much."
Anderson went 7-3 last season, but has struggled in five starts and was optioned to Triple-A Columbus on April 27. The right-hander has allowed 40 hits, including seven home runs, in 25 innings.
Anderson pulled up with leg cramps after throwing a pitch in the fifth, but remained in the game after Francona and a trainer went to the mound.
Moustakas, who leads the Royals with seven homers, originally was hurt April 26 while tagging out C.J. Cron of the Angels. He attempted to play through the pain until Wednesday, when he went 0 for 3 against the Nationals, and was a late scratch Friday.
Yost apparently has the ability to predict the future. The manager, speaking to reporters before the game, said, "Morales has been hitting rockets lately, but he doesn't have anything to show for it because he's hitting them straight at guys. I'm not concerned about him at all. That'll turn around and he'll start getting hits soon."
Royals: Moustakas will be examined by Dr. Thomas Graham, a hand specialist based in Cleveland while the Royals are in town.
Indians: OF Michael Brantley, who had offseason surgery on his right shoulder, was out of Saturday's lineup after starting the last four games.
Royals: RHP Edinson Volquez has lost his last two starts, despite pitching a season-high 7 2/3 innings Monday against Washington. He hasn't lost three straight decisions since 2014 while pitching for Pittsburgh.
Indians: RHP Josh Tomlin has won his first four starts. He held Detroit to two runs in six innings Tuesday. Tomlin has won 11 of his last 13 decisions dating back to last season.
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