Thames, who was playing only because regular designated hitter Gary Sheffield was serving the last of a two-game suspension, hit a solo homer with two outs in the eighth for the only run of the game in a 1-0 loss to the Tigers in front of 41,078 fans at Comerica.
"There's really no break in this lineup, without a doubt," Baker said. "You just look at the numbers for these guys, and they're pretty overwhelming."
Overwhelming for a guy who entered the game with a 2-2 record and 5.77 ERA, but has settled down in his last two outings. He gave up one run over seven innings in his last start against the Blue Jays on June 26.
"He's a different pitcher than when he first came back up here," manager Ron Gardenhire said of Baker, who was put into the starting rotation on May 19. "He's got a different attitude, different feel about him and he's been carrying himself very well. He's been showing it, the last two have been very good outings."
"He understands what he needs to do out on the mound now. He's not standing out there taking his time and doing all those things."
But Sunday night was probably the better of those two performances. He allowed just three hits on 79 pitches over eight innings for the first complete game of his career.
"If you were to hear that [line score] before the game, you would think that the outcome of the game would be different," Baker said. "It just wasn't tonight."
Baker retired the first nine batters in order to begin the game, five of those outs came on groundouts to shortstop Jason Bartlett. He needed just 25 pitches to get through the first three innings until he allowed his first hit to lead off the next inning.
Curtis Granderson led off the fourth with his league-leading 15th triple of the season, but Baker retired Polanco, Ordonez, as well as former All-Star Sean Casey, to leave Granderson stranded on third base.
"He really only left two balls up -- the Granderson triple and -- then Thames hit one out of the ballpark," Gardenhire said. "Other than that, he was lights out."
He again worked through the bulk of the Tigers order in the seventh to keep the game scoreless. Polanco led off the inning and reached on an error by Bartlett. Baker struck out Casey but allowed a single up the middle to Ordonez that put runners on first and second with one out.
Unfazed, Baker got another All-Star, Carlos Guillen, to ground into an inning-ending double play.
"It still comes down to good pitches get good hitters out," Baker said. "I was able to make good pitches in those situations."
While Baker had a few close calls -- Thames drove a ball about three feet short of a homer two innings before his long ball -- Baker's next pitch to Thames proved to be his only mistake. Thames swung at the first pitch of the fateful at-bat and deposited the ball over the wall and into the left-field bullpen.
"I wouldn't say it was a great pitch, it just ran back over [the plate] and he put a good swing," Baker said. "Basically there you are."
"I did a lot of things right tonight, it's disappointing when one pitch can determine a game."
While Baker was a model of efficiency, he threw just 56 pitches through six innings, Jeremy Bonderman was equally effective in his own way. Bonderman allowed six hits and over eight innings on 110 pitches but held the Twins scoreless over eight innings.
"I think he threw his fastball early on that was 88-89 [mph] all the way up to 96 [mph]," Gardenhire said of Bonderman. "It looked like he was adding and subtracting with it and making the ball dive. Great stuff tonight."
It was the sixth time the Twins had been shutout this season, the first since a 1-0 loss to Joe Blanton and the A's on June 2.
Even though a win would have given the Twins a three-game sweep over the Tigers, Gardenhire seemed pleased before the team boarded a plan for New York and a showdown against Roger Clemens on Monday.
"Very, very good baseball game. Very clean," Gardenhire said of the two hour, 17-minute game time. "We had a great series here, just unfortunate we couldn't get a run today."