Over seven innings, the left-hander (2-0, 0.61 ERA) limited the Twins to two hits and one run while walking two and striking out seven.
According to Elias Sports Bureau, Rodriguez is the first pitcher in modern Major League history (since 1900) to go seven innings in his first two starts while allowing as few as three hits and one earned run. He is also the first since 1920 to have at least seven strikeouts while allowing three hits or fewer in his first two starts.
When Rodriguez was called up from Triple-A Pawtucket last week, it was supposed to be for one start so that the other pitchers in the rotation could get an extra day of rest.
But there was no chance he would be sent down after the way he pitched in Texas. And there's certainly no chance he's going down now. How long will the Red Sox go with a six-man rotation? Who becomes the odd man out in to make room for Rodriguez? Those questions will be answered in time.
Next up for Rodriguez will be a matchup with the Orioles next week at Camden Yards. The Red Sox acquired Rodriguez from Baltimore for Andrew Miller last July 31.
"If he goes to Pawtucket, it's only on the way to Baltimore," Red Sox manager Farrell quipped.
The 22-year-old Rodriguez sure seems to have a future in Boston. Does Rodriguez -- ranked as the club's fourth-best prospect -- already exude the traits of someone who can be special?
"He does," Farrell said. "And I think anybody in the game who has watched Eddie pitch, whether it's been previously with Baltimore or since coming over here, we have the vantage point of getting to know the person in addition to the pitcher, and he's got great aptitude, he's intelligent, in addition to the physical abilities that he demonstrates. He's a special kid."
Rodriguez doesn't just have filthy stuff, but also possesses the poise required to succeed at the highest level.
The one time Rodriguez found himself in trouble on Wednesday was in the sixth inning, when he gave up a single and a walk. But he settled down quickly, getting a flyout and two groundouts.
"Two things stood out in that game," Farrell said. "After [Brian] Dozier's solo home run, he's right back in the strike zone, not fearing contact. And then in that sixth inning, after the two leadoff men get on base, he got extended in the [Shane] Robinson at-bat, but still, continued to throw a good number of strikes. He battled through, pitches out of a potential jam."
Rodriguez is staying humble about his accomplishments.
"I just tried to do the best I can, throw strikes, kept my pitches down in the zone," Rodriguez said. "My slider was working pretty good with the outside corner and inside corner. My changeup was pretty good, too. My two-seamer, my fastball was pretty good."
The Red Sox are enjoying playing behind the newest member of the rotation, who threw 77 of his 103 pitches Wednesday for strikes.
"I mean, pretty impressive," said shortstop Xander Bogaerts. "I faced him one time I remember in Spring Training when he was with the Orioles. That's as much as I know. Coming up, these two starts, the thing I've been most impressed by is how he's been getting ahead in the count, just throwing strikes. I think I looked up at the board and he had like 75 percent of his pitches were strikes. When I saw that, I couldn't believe that."
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.