In the eighth, Tim Collins missed a fastball location, and Chris Iannetta homered to left field for the difference in the Angels' 4-3 comeback victory.
So the Royals, who took a 3-0 lead in the third inning, lost their first series-deciding game this season, after starting 3-0 in those situations. The Angels took two of three games, with the Royals winning Saturday's 13-inning marathon, 7-4.
"I just missed," Collins said of the pitch Iannetta drove out. "I was trying to go away. You can't miss your spots in those situations. That's what I did, and that's what happens."
Herrera had worked 14 consecutive scoreless outings and owned a 1.21 ERA when he took over for Vargas with one out and one on in the seventh. He gave up a pinch-hit single to Raul Ibanez. An out later, Mike Trout touched Herrera for an RBI double down the third-base line for the lone run charged to Vargas.
Herrera then hit Albert Pujols with a pitch to load the bases. David Freese's two-run single to center tied the score at 3. C.J. Cron followed with a single, but right fielder Lorenzo Cain threw Pujols out at the plate -- a call that stood after an Angels challenge.
"[Herrera] couldn't put them away," manager Ned Yost said. "He was ahead of guys, and then he couldn't make a good pitch.
"I kept thinking, 'He's gonna make a pitch. His stuff is good.' He was throwing 97, 98. He got [Howie] Kendrick to fly out. He got hit on two curves and he hit Albert with a changeup."
According to Collins: "[Herrera] has been great all year. He had a rough day today. That's the way it is. You can't be lights-out every day."
Vargas, facing the team he pitched for last season, wasn't exactly lights-out, but he was effective despite a season-high five walks. He had allowed just two infield singles before Iannetta got one to the outfield to open the seventh, and he struck out six. Vargas stayed on to retire the left-handed-hitting Kole Calhoun before it was Herrera's turn.
"Any time you lose a game like that, it's frustrating," Yost said. "The way Vargas pitched, it's frustrating to lose it, too. He was working around hitters, got out of trouble. They have a packed lineup over there. He was extra-careful with Pujols, Trout, [Kendrick]."
Right-hander Wade Davis, who threw two shutout innings on Saturday, warmed up. But Yost went to his left-hander, Collins, in the eighth with a switch-hitter and two lefties due up among the first four hitters.
"Wade was going to pitch the ninth if it was still tied," said Yost, who before the game said he wouldn't use righty Aaron Crow, who pitched two innings Saturday and one Friday.
"I was just missing. I wasn't able to get ahead of some of those guys and walked them real quick. You've got to make quality pitches to a lot of guys in that lineup," Vargas said of his five walks, which ran his pitch count to 109.
The Angels' Mike Scioscia, Vargas' manager in 2013, said: "I thought we did a good job on Jason. We got the leadoff man on the first four innings. We pressured him, set the table, but didn't get the big hit early. We got it late with David Freese, [Trout] -- and Chris hits the huge home run."
The Royals scored all their runs off Angels starter Garrett Richards in the third inning, with some new contributors getting it started.
With one out, Jimmy Paredes singled, his first hit for Kansas City. Pedro Ciriaco doubled him in for his first RBI in 32 at-bats with the Royals, for whom he also played briefly last year. Ciriaco's last Major League RBI was June 25 for the Padres against the Phillies.
After Jarrod Dyson's infield hit, Eric Hosmer's foul ball turned into a sacrifice fly, scoring Ciriaco, despite a fine, sliding-to-one-knee catch and throw by Angels left fielder Collin Cowgill. Billy Butler walked, and Alex Gordon delivered a two-out single to score Dyson.
"One more two-out hit, and it's 5-0," Yost said. "That's a good inning, but you've still got to find ways to tack on runs."
In the top of the seventh, Cowgill made another sliding catch, this time on a Paredes' foul fly, which was a little deeper, but no less a spectacular play.
The Royals (24-25) missed a chance to go over .500.
Asked if the end result was frustrating, Collins replied: "Isn't it always?"