Anderson allowed just two hits in seven scoreless innings, and Francisco Lindor and Jose Ramirez homered as the Indians beat the wild-card-chasing Twins 10-2 in the second game of a doubleheader at Progressive Field.
Gibson (11-11) pitched six scoreless innings of four-hit ball while matching his career high with nine strikeouts.
Losing the second game prevented the Twins from taking a big step in the race for the second American League wild card. They began the day one game behind Houston and 1 1/2 games behind Los Angeles Angels. Fortunately for the Twins, the Angels also lost Wednesday night. The Astros were playing a late game.
"We didn't get a sweep, but the Angels didn't win, they finally had a hiccup," Twins manager Paul Molitor said. "We're a game behind them, but we live for another day, that's for sure."
In the second game, Anderson was nearly unhittable. The rookie right-hander the season with a 7-3 record and a 3.05 ERA in 15 starts. In his last five starts, he went 5-0 with a 1.09 ERA.
"He's commanding his fastball, he has that changeup, and he's down in the zone with everything," Indians manager Terry Francona said.
The Twins failed to get a runner as far as third base against Anderson. The only hits he allowed were a single by Hunter in the second inning and a single by third baseman Trevor Plouffe in the sixth.
"The way he competes and the way he acts on the mound, he has a very bright future," Francona said of Anderson.
The Twins' only runs came on solo home runs by designated hitter Miguel Sano in the eighth inning and left fielder Eddie Rosario in the ninth.
Leading 7-1, the Indians added three more runs in the eighth inning on a three-run homer by Ramirez off right-hander Ricky Nolasco. The Cleveland second baseman sparked some controversy by admiring his home run before running to first base, then flipping his bat toward the Minnesota dugout.
Molitor and several Twins players could be seen yelling at Ramirez as he rounded the bases and crossed home plate.
"Some of our people thought that was over the top and disrespectful, so we reacted," Molitor said.
Nolasco was less diplomatic.
"To pull a (garbage) move like that, he'll get his, don't worry," Nolasco said.
Said Francona: "Good swing, poor judgment. Hitting the home run was good enough. He'll learn. Hopefully not the hard way, but he'll learn."
Twins right-hander Mike Pelfrey (6-11), whose last win was Aug. 12, started but didn't stick around for long. He pitched 1 2/3 innings, giving up four runs, six hits and two walks.
In eight starts since his last win, Pelfrey is 0-4 with a 6.31 ERA.
Center fielder Abraham Almonte led off the second inning with a double to center. Catcher Adam Moore struck out, but left fielder Michael Martinez singled to score Almonte. A throwing error by center fielder Aaron Hicks allowed Martinez to go to second.
Designated hitter Jason Kipnis lined out to short for the second out. However, Ramirez doubled to left field, scoring Martinez to make it 2-0.
Shortstop Francisco Lindor reached on an infield single, moving Ramirez to third. Ramirez scored on a wild pitch by Pelfrey, and a single by first baseman Carlos Santana scored Lindor to make it 4-0.
An RBI single by Moore in the third inning and a two-run homer by Lindor in the fourth stretched the lead to 7-0, and the rout was on.
Cleveland right-hander Carlos Carrasco (14-12) took the loss in the opener, allowing five runs in three innings.
NOTES: Twins OF Torii Hunter is hitting .444 (12-for-27) with five doubles, three home runs and 11 RBIs at Progressive Field this year. ... RHP Kyle Gibson has made 73 career starts for the Twins. The Twins won 35 of those games, and in those contests, Gibson has a 1.65 ERA. ... SS Francisco Lindor is just the third Indians rookie to have 10 or more home runs and 10 or more stolen bases in a single season. The other two were Earl Averill in 1929 and Von Hayes in 1982. ... Indians 2B Jason Kipnis has 18 three-hit games, the second most in the American League behind Jose Altuve's 20.