The Blue Jays, who topped the majors with 891 runs in the regular season -- 127 more than any other club -- were limited to three singles. The Blue Jays were shut out only five times during the regular season.
Volquez limited the Blue Jays to two singles over six innings, but had to work around four walks. Cueto limited the Houston Astros to two hits over eight innings in the ALDS clincher Wednesday.
"We're friends and I see what he did the other day and I was like it was time for me to do something good, especially in playoffs," Volquez said. "Besides tonight I haven't won a game in playoffs and I got one tonight. I think I got a little bit of motivation from him."
Volquez was 0-3 with an 8.76 ERA in his first three career postseason starts.
"Eddie was superb, had everything going on, had his great fastball, locating well, really good curveball, really nice changeups, on the attack from the first inning on," Royals manager Ned Yost said.
Volquez weaved through a treacherous sixth inning, throwing 37 pitches and reaching full counts on four batters. He walked Josh Donaldson to start the inning. He had Jose Bautista down in the count 0-2 and he fouled off the next two pitches. Bautista wound up drawing a walk on nine pitches. That brought up Edwin Encarnacion, who struck out looking.
Volquez walked off the mound with 39,753 fans standing and chanting, "Eddie, Eddie, Eddie."
"They gave me more energy to pitch the way I pitched in that inning," Volquez said.
With Volquez's pitch count at 111, Kelvin Herrera took the baton in the seventh. He threw nine pitches, all strikes, in retiring the Blue Jays in order, striking out two.
"It's just one game," Madson said. "We've got to win three more to be happy about anything."
The Blue Jays bigger concern than losing the first game is the health of Encarnacion, who was pinch hit for in the eighth inning to have X-rays of his middle left finger, which has been bothering him for a while. X-rays were negative.
"But it swelled up a little bit more than we've seen it in the past," Blue Jays manager John Gibbons said. "Usually a day or two, it calms down on him and he's able to get through it. It's an early game tomorrow, hopefully, he'll be able to go."
The Royals opened the scoring with two runs in the third. Gordon started the inning by pulling a Marco Estrada 91 mile per hour fastball into the right-field corner. After one out, shortstop Alcides Escobar hit a ground-ball double to right on an Estrada curveball, scoring Gordon. Escobar, a notorious first-pitch swinger, doubled on the first two Estrada pitches he viewed.
"Always, I swing the first pitch," Escobar said. "And then he throws me a curve and I swing again. When I swing at the first pitch, we're like 40-19. Everyone says just continue to swing the bat."
Center fielder Lorenzo Cain's two-out single brought Escobar home. Cain extended his postseason-hitting streak to 11 games, one shy of the Royals' record held by Amos Otis.
The Royals hiked their lead to 3-0 in the fourth when catcher Salvador Perez homered on Estrada's first offering over the left-center fence after two out.
The Royals padded their lead in the eighth with an Eric Hosmer double scoring Escobar, who was hit by a LaTroy Hawkins pitch to lead off the inning. Hosmer's laser double came within inches of clearing the right-field field fence.
"I got in a hitters' count and was just trying to drive the ball there and get some extra runs in," Hosmer said. "We know how tough that lineup is over there. Insurance runs were big for us.
"I thought it was a good chance of getting out. I actually thought it hit the back wall and came in. That's baseball, a game of inches."
Kendrys Morales' sacrifice fly scored Ben Zobrist, who had reached on an infield stop and stopped at third on Hosmer's double.
Estrada, who led the American League by holding hitters to a .203 average in the regular season, gave up three runs on six hits in 5 1/3 innings.
Royals pitchers have thrown 16 consecutive scoreless innings.
"I guess it was a combination of things," Blue Jays first baseman Chris Colabello said. "We got some guys on base at certain points in time. I don't think Volquez's strikeout total was high. Obviously we were putting some balls in play. We hit some balls at guys. That's just the way it goes sometime."
"Volquez picked his spots obviously. I don't feel like there isn't a night when our big guys--Jose, Eddie and Josh--where you can feel comfortable going in. Tonight, the ball wasn't really flying much. We noticed that in BP. He kind of mixed it up. He used his change-up well. That's kind of who he is."
NOTES: C Dioner Navarro was in the Blue Jays' lineup, not C Russell Martin, as he developed into RHP Marco Estrada's personal catcher. ... LHP Brett Cecil, who suffered a left calf injury in the ALDS, was not on the Toronto ALCS roster. RHP Ryan Tepera replaced Cecil. ... The Royals went with the same roster as they did in the ALDS series against Houston. ... Royals manager Ned Yost said he does not yet have a Game 4 starter. The likely candidates are RHP Kris Medlen or RHP Chris Young. ... Blue Jays LHP David Price and Royals RHP Yordano Ventura are the starters Saturday. ... The Royals and Blue Jays met in the 1985 postseason, with Kansas City rallying from a three games-to-one deficit to win the series.