CINCINNATI -- If Wednesday's game was Johnny Cueto's last as a Cincinnati Red at Great American Ball Park, he made it memorable.

The Cincinnati right-hander, who's in the last year of his contract and is considered to be prime trade bait for the struggling Reds, engaged Minnesota's Trevor May in an old-fashioned pitchers' duel Wednesday in a game decided by a throwing error on a throw that didn't need to be made.

Cueto posted his longest outing since missing his last two starts of May with a sore right elbow as the Reds squeezed out a 2-1 win over the Twins in the rubber match of the three-game series before a crowd of 26,459.

Despite pitching with such a narrow edge and with speculation swirling around him, Cueto (5-5) said through assistant trainer and interpreter Tomas Vera that he was able to maintain his focus.

"I've just got to keep going out there and pitching and leave everything else in God's hands," Cueto said. "I always thank God for everything. When I go out there, all I think about is pitching. Right now, I'm pitching for the Reds.

"I'm always relaxed. I try to keep everything normal. I'm always relaxed when I pitch."

The teams combined to produce 51 hits and 31 runs in the first two games of their interleague series.

Cueto, a 20-game winner last season, allowed four hits and one run, with one walk and eight strikeouts, over eight innings. He allowed just one runner past second base while throwing 111 pitches, 74 for strikes, in what manager Bryan Price considered to be a vintage performance.

"He was terrific," Price said. "It's not like it's something we haven't seen before. We've seen it lots of times. He takes the game and runs with it. One thing he was able to do was make it a restful day for the bullpen. What Johnny did was allow our bullpen to catch up on its rest."

The Reds (36-41) bounced back after being swept by the Mets in a three-game weekend series at New York by taking two out of three from the team that went into Wednesday's game second in the American League Central Division, 4 1/2 games behind Kansas City.

The Twins (41-37) left after the game for Kansas City, where they are scheduled to conclude their 10-game trip with a four-game series against the Royals, starting Thursday.

Aroldis Chapman pitched the ninth for his 16th save in 17 opportunities and his 53rd straight at Great American Ball Park since blowing a chance against Houston on Sept. 7, 2012.

Reds center fielder Billy Hamilton clinched the win with a diving catch to his left of pinch hitter Torii Hunter's line drive.

May (4-7), who allowed six runs while logging just one out in his last start on June 26 at Milwaukee, lasted 6 1/3 innings Wednesday. He gave up six hits and two runs (one earned), walked three, struck out six and threw two wild pitches.

Like Cueto, staying calm was May's approach.

"That was the overlying theme for me today -- just kept telling myself, and sometimes I'd say it out loud, 'You're one pitch away, one pitch away,'" May said. "I just tried to do that as well as I could."

May has lost four straight decisions in five starts since his last win on June 3 at Boston.

The Reds squandered a golden scoring opportunity in the second inning before pushing across a run in the third. Second baseman Brandon Phillips led off with a double into the left-field corner and went to third on a wild pitch, setting up first baseman Joey Votto's sacrifice fly.

That was one inning after loading the bases with nobody out on three singles, only to see shortstop Eugenio Suarez and Cueto strike out and Hamilton fly out.

The impact of Hamilton -- the major leagues' stolen-base leader -- never was more apparent than in the bottom of the fifth. Hamilton, who went into the game with 40 stolen bases in 46 tries, was on second with Phillips on first and took off for third as May was delivering Ball 4 to Votto. Instinctively, backup catcher Chris Herrmann threw to third, overthrowing third baseman Trevor Plouffe for an error that allowed Hamilton to score.

Herrmann thought the pitch was Strike 3, manager Paul Molitor said.

"He thought he might get that call, so he comes up firing and the ball goes into left field," Molitor said. "Chris had already committed to making the throw."

The Twins broke up Cueto's shutout bid in the sixth on second baseman Brian Dozier's leadoff double, shortstop Eduardo Nunez's runner-advancing groundout and right fielder Eddie Rosario's RBI groundout.

NOTES: The Reds announced a scoring change from their 8-5 loss to Minnesota on Tuesday. Cincinnati's Billy Hamilton was credited with an infield single on what previously had been ruled an error by SS Eduardo Nunez. ... Twins LF Shane Robinson, scratched from Tuesday's starting lineup with a stomach ailment, returned to the lineup Wednesday. ... Reds 2B Brandon Phillips started and batted leadoff in his first action since leaving Sunday's second game against the Mets in New York with injuries to both hands. ... Cincinnati RHP Raisel Iglesias pitched three innings for Triple-A Louisville on Tuesday in his first appearance since going on the disabled list on June 15 with a strained left oblique. He is expected to make two more rehab starts. ... Reds LHP Tony Cingrani is scheduled to pitch two innings in a rehab assignment Friday. Cingrani has been on the disabled list since June 15 with a strained left shoulder. ... The Anderson Monarchs, the Little League team for which Mo'ne Davis became the first girl to win a game at the Little League World Series last year, were honored on the field in pregame ceremonies. Davis and her teammates are on a tour of historic civil rights sites.