Griffin has now made four starts, pitched 25 innings and is 3-0 with a 2.52 ERA. Those are the same numbers that Cole Hamels has after his first four starts. There are a few differences, though, such as the fact that Griffin has allowed three fewer hits and two fewer walks.
Griffin on Tuesday also turned in the longest start by a Rangers pitcher this season, going eight innings, and he allowed one run on four hits and a walk while striking out five.
In doing so, he helped the Rangers snap a four-game losing streak.
"That's pretty weird," Griffin said of the similarities with Hamels. "Like I said, my expectations are high. If you ask anything less, it opens the door for less favorable things to happen, so I go out there and try to get every guy out."
High expectations are admirable, and Griffin was a 14-game winner for the Athletics in 2013, but this is a pitcher who missed the last two seasons recovering from Tommy John surgery and had to fight down to the last week of Spring Training to win a spot in the rotation.
"I feel like I'm back," he said. "My mechanics are sound and all my pitches are working the way I want. It's pretty exciting stuff."
Griffin's outing came on the same day Darvish threw possibly his last batting-practice session in his own recovery from Tommy John surgery. Darvish could be ready to return to the rotation before the end of May, and the assumption has been that he would step in for the fifth starter.
Griffin is altering those assumptions.
"All I can do is pitch as well as I can," Griffin said. "Whatever happens, happens. You've got to live with what happens. If you're not trying to make a case for yourself, you're not doing the right thing."
Manager Jeff Banister said that Griffin doesn't need to be thinking about that right now.
"Obviously, he is making a strong case for himself every time out," Banister said. "We're seeing what he is able to do when he is healthy, and he is healthy now. I'm proud of where he is, based on the history."
On Tuesday, Griffin retired 16 of the first 17 batters he faced and allowed just two singles through six innings. A leadoff walk and two singles in the seventh sent home the Yankees' only run, but Griffin cut that rally short by getting catcher Brian McCann to ground into a double play.
"We should have put better swings on his mistakes, but he didn't have many," said Yankees designated hitter Mark Teixeira, who recorded his team's only RBI.
Griffin is now 3-0 with a 2.49 ERA in four career starts against the Yankees.
"It just seemed like he mixed speeds," Yankees manager Joe Girardi said. "He mixed in and out, up and down, used that really slow curveball. It looked like his slider was really effective tonight. Sometimes I can't tell if it's a slider or a change from where I'm standing, but he seemed to use both. He just seemed to stay out of bad counts and out of the middle. He stayed down."
Griffin is also making a case for staying in the rotation.
T.R. Sullivan has covered the Rangers since 1989, and for MLB.com since 2006. Follow him on Twitter @Sullivan_Ranger and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.