LOS ANGELES -- Dodgers ace Clayton Kershaw pitched 4 1/3 innings in a Minor League rehab start on Thursday night at Oklahoma City against the Brewers' Triple-A affiliate. Kershaw allowed two runs on four hits with six strikeouts, two walks and a pickoff.

Kershaw, recovering from spring shoulder soreness, allowed both San Antonio runs in a 21-pitch second inning, when he allowed a home run. He finished making 61 pitches (42 strikes), one more than the target. At one point, he struck out five of seven batters.

"It was a good first step," Kershaw said. "I kind of got through everything I needed to, got up for that fifth inning, got some guys on base, worked out of the stretch, did multiple different things. ... I came out of it feeling good, ready for the next one."

Manager Dave Roberts said this week he was leaning toward Kershaw making a second rehab start next week before returning to the Dodgers' big league rotation.

Kershaw walked San Antonio leadoff batter Corey Ray in a nine-pitch at-bat, but he picked Ray off first base and faced only three batters with one strikeout. Tyrone Taylor ambushed Kershaw’ first pitch of the second inning for a homer down the left-field line. Before the inning was over, Kershaw had allowed another run and issued his second walk, but also struck out two more.

In the third inning, Kershaw struck out the side, pitching around an infield single and throwing error by third baseman Edwin Rios. In his fourth, Kershaw allowed a leadoff single, but a double-play grounder led to a 10-pitch inning. Kershaw came out for the fifth inning and retired Jacob Nottingham on a groundout to shortstop before exiting.

Kershaw, who signed a three-year, $93 million contract in November, spent the offseason recalibrating his body to better sync with his mechanics after experiencing a drop in fastball velocity.

His first two bullpen sessions in Spring Training went without a hitch and he had already been named the Opening Day starter for a ninth consecutive season, but after a live batting-practice session and a bullpen session two days later, Kershaw complained of shoulder discomfort.

He received anti-inflammatory medication and treatment and was shut down for several days, followed by 10 days of throwing that led to the pair of bullpen sessions.

Although he’s been healthy for several weeks, the interruption in his buildup prevented him from pitching any Spring Training games and landed him on the injured list for the fourth consecutive season. He threw a 50-pitch simulated game on Saturday that set him up for Thursday’s start.

The last time Kershaw began his season in the Minors was on April 4, 2008, with the Double-A Jacksonville Suns. He took the loss in the team’s 6-3 defeat against the West Tenn Diamond Jaxx.