These left-handers square off Wednesday night with Rodriguez trying again for his first victory with the Pirates and Kershaw taking another shot at beating Pittsburgh for the first time.
Kershaw (10-6, 2.88 ERA) has been strong for most of the year, but he's been especially sharp in winning his last three starts. He has posted a 1.21 ERA in that stretch, striking out 21 and walking four over 22 1-3 innings.
"He has really been good almost every time out, but he's getting in a little bit of a groove, it seems like," manager Don Mattingly said Friday after Kershaw yielded three hits in 6 1-3 innings of a 5-2 win at Miami.
Kershaw is 0-1 in five career starts against the Pirates, although he probably deserved a victory against them April 10. He allowed one run and four hits in seven innings of that game, but left with the score tied before the Dodgers won 2-1.
His three starts in Pittsburgh haven't gone as well. Kershaw hasn't worked more than five innings in any of them, posting a 3.95 ERA, although he hasn't pitched there since April 7, 2010.
Rodriguez (7-11, 3.91) pitched at PNC Park for the first time in a Pirates uniform Thursday, allowing four runs in six innings of a 6-3 loss to Arizona. He was leading 3-2 entering the sixth, but Wil Nieves belted a two-run homer with two outs.
That dropped Rodriguez to 0-2 with a 4.74 ERA in three outings since Pittsburgh acquired him from Houston last month. In the last two - both losses - he's allowed seven runs entirely on four homers.
"I don't know what's going on with me - I've lost the last two games on only one pitch," said Rodriguez, who is 0-5 with a 5.66 ERA in six starts overall since the All-Star break.
Perhaps facing Los Angeles will help. Rodriguez has a stellar 2.24 ERA in 11 career starts against the Dodgers, limiting them to three hits over seven innings in a 12-0 win for the Astros on April 22.
Andre Ethier is 3 for 20 (.150) against Rodriguez and Matt Kemp is 5 for 21 (.238), but Hanley Ramirez could throw a wrench in that dominance. During his time with the Marlins, Ramirez was 9 for 22 with four extra-base hits against Rodriguez.
The Pirates (64-52) are desperate for a stopper, having lost five of six - all at home - with their starters posting a 7.15 ERA in that stretch. They have dropped the first two in this four-game set, and their lead for the second NL wild card is down to one-half game over co-West leaders Los Angeles and San Francisco and one game over St. Louis.
"This is our worst patch of play probably during the season," manager Clint Hurdle said. "Every team that I have been on has a patch of play like this. We know what we are dealing with and we have to find a way to turn it around."
The Dodgers (64-53) have won five of six, taking Tuesday's game 11-0 behind an impressive outing by Chad Billingsley and a 3-for-5, three-RBI performance from Luis Cruz. Ramirez was 3 for 5 with two RBIs, his third multihit game in the first five contests on this road trip.
"You've got everybody chipping in," Ramirez said. "Not only one guy, the whole team is going out there and contributing."