Kuroda looks to continue his recent success Tuesday night while trying to help New York hand the Rangers a seventh straight loss in the Bronx.
"I think it's extremely important, because the two best records in the American League are the teams that are playing (in this series)," manager Joe Girardi told the Yankees' official website. "These games could determine a lot."
Winners in five of six overall, the East-leading Yankees (68-47) have outscored the Rangers 46-19 during a six-game home winning streak in the series that dates to a 5-3 Texas victory April 15, 2011.
Texas (67-47) could find trying to end that skid an even more difficult challenge against Kuroda (10-8, 3.24 ERA), who is 2-1 with a 1.82 ERA in his last five starts. He's also allowed three runs in 21 1-3 innings while going 1-1 in his last three at home.
Kuroda gave up three runs - the most he's allowed during the last five starts - and 10 hits in 6 1-3 innings while not factoring in the decision of a 4-3 win at Detroit on Thursday.
The right-hander is 0-2 with a 4.50 ERA in two starts against the Rangers, but he surrendered two runs and five hits in 6 2-3 innings of a 2-0 loss at Texas on April 24.
Teammate Eric Chavez has homered in each of his last two games, and is 11 for 20 with three and six RBIs over his last five.
Swisher, who has two grand slams this season, is batting .367 (11 for 30) with eight RBIs in his last seven games. He is 4 for 10 against scheduled Texas starter Matt Harrison (13-6, 3.31).
Though the left-hander leads the Rangers in wins, he is 1-2 with a 5.55 ERA in his last four starts. Harrison is feeling much better than he did Wednesday, when he battled a virus while giving up five runs, eight hits and three walks in 4 2-3 innings of a 10-9 win at Boston on Wednesday.
"I feel good. I'm ready to rebound from my last start and go out and do my job," Harrison the Rangers' official website. "The biggest thing is I didn't have any energy."
He is 2-2 with a 4.26 ERA as a starter against the Yankees.
"It's never fun to make baserunning mistakes,'' said Murphy, who is 6 for 15 in his last four games in the Bronx. "We run the bases aggressively and sometimes it really works out for us and sometimes it doesn't.''
Cruz is batting .448 (13 for 29) in the last eight games but is 1 for 6 versus Kuroda.