Rangers-Red Sox Preview
Now, it's Grimm who has started to settle in with the Rangers and Dempster still seeking consistency in his first campaign with the Red Sox.
The right-handers will face off Tuesday night as Boston hosts Texas in the opener of a three-game set between first-place teams.
Grimm (5-3, 3.93 ERA) was a 13th-round selection out of high school in 2007 by the Red Sox (35-23), but he didn't sign and opted to play for the University of Georgia for three years before being drafted by Texas (35-21) in 2010.
He pitched five times for Texas last season and was only initially called up this year when Matt Harrison was placed on the disabled list in April. Now, Grimm leads all AL rookies in wins and has victories in his last three starts with a 3.32 ERA.
"He's gotten better as far as confidence-wise, believing and knowing that he belongs here," catcher A.J. Pierzynski said after Grimm gave up two earned runs over six innings to beat Arizona 9-5 on Thursday.
"It's just a progression with young guys. He continues to get better. You can see it in his face. You can see it when he takes the mound in his mannerisms."
Dempster (2-6, 4.45) has been tagged with a loss in four of his last five outings while amassing a 6.41 ERA, though he gave up two runs in seven innings of a 3-1 defeat to Philadelphia last Tuesday.
He was 7-3 with a 5.09 ERA in 12 starts last year for the Rangers, who acquired him from the Cubs prior to the trade deadline.
"He's a great competitor," Texas shortstop Elvis Andrus told the team's official website. "He's going to go out there and try to get you out. He's got great stuff. It's going to be good to face him again."
Trying to back up Grimm will be Jurickson Profar, who provided the go-ahead home run in the eighth inning of Sunday's 3-1 win over Kansas City. The 20-year-old rookie is hitting .324 in 10 games since being called up to fill in for injured second baseman Ian Kinsler.
Both lineups could be bolstered with the returns of everyday players.
Boston outfielder Jacoby Ellsbury sat out last weekend's series against the Yankees with tightness in his left groin, but the team is hopeful he'll be ready to go after Monday's off day.
Rangers third baseman Adrian Beltre is 16 for 38 (.421) over his last nine games but missed Sunday's contest with a mild left hamstring strain, an injury he aggravated while running the bases in Saturday's 4-1 loss.
"It might be Wednesday, but Tuesday is realistic," manager Ron Washington told the Rangers' official website. "The thing is, he'll be back in there soon."
Red Sox first baseman Mike Napoli, who is 10 for 24 with eight RBIs over his last seven games, went 1 for 10 with four strikeouts against his former team as Texas swept three home matchups while outscoring Boston 16-4 from May 3-5.
David Ortiz has at least one hit in 14 of his last 15 games against the Rangers, hitting five home runs and driving in 11.
Ortiz and Napoli each homered as Boston took two of three in New York, including a 3-0 victory that was stopped after 5 1/2 innings because of rain Sunday night.
Texas has won 11 of the last 14 overall meetings and 10 of 13 at Fenway Park.