The two pitchers will oppose each other when their teams begin a three-game series on Friday at Dodger Stadium.
Kershaw and the Dodgers are cruising along and seemingly hitting on all cylinders, having led in the National League West most of the season.
Harrell is an inexperienced but talented right-hander for a young Astros team that has show some spark and hope for the future after a dreadful 2011.
Kershaw's 4-1 record might not excite anyone who has not been paying attention, but the talented left-hander also has a 1.90 ERA in nine starts and is coming off a commanding 6-0 victory over Cardinals and their hard-hitting lineup in his last outing on Saturday.
It was the first shutout of the season for Kershaw, who limited the Cardinals to six hits.
The performance capped off a week in which Kershaw earned the NL Player of the Week Award after winning both of his starts.
In his previous start, the 2011 Cy Young Award winner pitched seven shutout innings while allowing four hits and striking out six in the Dodgers' 3-1 win over Arizona.
Los Angeles has raced out to a best-in-baseball 30-14 record and a seven-game lead in the NL West. Manager Don Mattingly said it's been a matter of having success, feeding off of it, and in turn having more success.
"Things are just going good for us right now," Mattingly said. "We've just got momentum right now. Guys are stepping up. "If we can hang in there and win games, that feeds on itself. But the game is funny, it can go in the other direction, I don't forget that."
Prior to this season, Harrell had just five Major League starts. Now, he's scheduled to make his 10th start of the season against the Dodgers.
Harrell is 3-3 with a 4.09 ERA and won his last start Saturday against the Rangers, overcoming an error behind him that led to three unearned run in a 6-5 victory.
Harrell went 5 1/3 innings and allowed five hits while striking out six.
The Astros, who have won three straight and seven of their last 11, have the ability to bounce back successfully from adversity, Harrell said.
"This team fights," Harrell said. "I've said it all year. We don't quit and there's a lot of fight in us, and we've got a young guys that are hungry, and we want to win."
Mills said that Harrell is improving at controlling his emotions and fighting back from adversity.
"He's very competitive and he wants to be out there and he will be out there," Mills added.
Astros: Sitting third in NL Central
After Wednesday's 5-1 victory over the Cubs, the Astros are 21-23 overall, but in third place in the NL Central, four games behind the division-leading Cardinals.
Houston center fielder Jordan Shafer was out of the lineup after having part of the toenail on his right big toe removed on Wednesday. Schafer injured the toe last week when he fouled a ball off it. Mills said on Wednesday that he expects Schafer to be better in a couple of days.
Dodgers: Versatile Herrera stays hot
Elian Herrera, who had played second base and third since being recalled from Albuquerque on May 14, played center field Wednesday and had two hits in four at-bats, raising his average to .346.
The series will be the Astros' final trip to Dodger Stadium as a member of the National League.
The Astros, who are moving to the American League next year, played in the NL West from 1969-93 and the Dodgers were one of their biggest rivals.
The teams played a one-game playoff for the NL West title following the 1980 season, with the Astros winning.
Nolan Ryan threw his fifth no-hitter against the Dodgers in the Astrodome in 1981. The teams played an epic 22-inning game in the Astrodome on June 3-4, 1989, won by the Astros.
The Astros are 319-386 all time against the Dodgers, including a 143-215 mark at Chavez Ravine.