The visiting Dodgers have to like their chances of evening this three-game set Saturday night behind Greinke, whose teams are 6-0 in his outings against the Padres.
Greinke (13-8, 2.79 ERA) is 8-0 with a 1.79 ERA in 10 starts against division opponents and 5-8 with a 3.48 ERA in his other 16 outings.
The right-hander took advantage of two extra days of rest to limit the New York Mets to four runs in seven innings last Saturday in a 7-4 win.
"I thought I pitched really well," he said. "I felt great again today. And so hopefully that's how it stays."
Greinke is 9-0 with a 2.31 ERA in 13 road starts against NL West opponents with the Dodgers.
He is 4-0 with a 2.00 ERA against the Padres (63-70), limiting Jedd Gyorko and Alexi Amarista each to one hit in seven at-bats and Will Venable to two in 15. Seth Smith may be San Diego's biggest threat since he is 6 for 15 off Greinke although he is in a 1-for-23 slump.
Getting runs for Kennedy (10-11, 3.75) hasn't been easy - his 3.53 run support average is baseball's 10th-lowest mark.
He is a southern California native and USC product who went 5-2 with a 3.24 ERA in his first eight outings against the Dodgers (76-59) before going 0-4 with a 5.53 ERA in his next seven - including 0-2 with a 4.70 ERA in four this year.
The right-hander bounced back from an Aug. 19 defeat to Los Angeles by yielding three runs over 5 2-3 innings to earn Sunday's 7-4 win at Arizona.
"His breaking ball and his changeup, he mixed it in good," manager Bud Black said.
Carl Crawford is a .348 hitter against Kennedy and Andre Ethier is at .324. Faring poorly are Adrian Gonzalez (.212) and Hanley Ramirez (3 for 18).
This is the second meeting this season between these starters, who were part of a memorable brawl in which six players and coaches were ejected last June 11 when Kennedy was with Arizona and hit both Greinke and Yasiel Puig with pitches.
Puig, 3 for 15 against Kennedy, could be back in the starting lineup Saturday. He did not start in Friday's 3-2, 12-inning loss because manager Don Mattingly said the outfielder seems frustrated.
Puig is hitless in 17 at-bats after striking out as a pinch hitter Friday.
"He has to figure out his way and get ready," Mattingly told MLB's official website. "He needs the mental approach to keep his body good and his mind right. It's a balance."
Ethier made just his third start in the Dodgers' last 12 games in Puig's place. Justin Turner continues to shine, going 14 for 29 in his last eight games after a three-hit effort Friday.
Los Angeles' NL West lead over San Francisco was cut to 3 1/2 games.
Yasmani Grandal singled in the winning run for San Diego, which has won three straight against division leaders after taking two of three from Milwaukee earlier this week.