LOS ANGELES -- By the time Zack Greinke walked into Los Angeles Dodgers president Stan Kasten’s office last winter he had a pretty good idea of what he was walking into.

The Dodgers would probably make him the best offer of any of his free-agent suitors, he’d be supported by one of the National League’s most talented lineups, and for as long as he pitched in Chavez Ravine, the new ownership group promised seemingly unlimited financial resources.

What he didn’t count on or, rather, what he couldn’t possibly realize then the importance of, was the effect pitching alongside left-hander Clayton Kershaw would have on him.

“The team looked really good to me,” Greinke said after his latest masterpiece, a nine-strikeout, 6-2 win over the woeful Chicago Cubs Monday night.

“What I didn’t know was how good [Kershaw] was going to be. You knew he was going to be really good, but you didn’t know how good.”

Together, Greinke and Kershaw have formed the National League’s most potent 1-2 punch and pushed each other seemingly each and every time through the rotation. Greinke improved to 13-3 with a 2.86 ERA with Monday’s five-hit gem. Kershaw will start Tuesday’s game with a 13-7 record and a major league-best 1.72 ERA.

Greinke has now won five in a row. Kershaw has won three straight. Greinke pitched 8 2/3 innings of shutout ball Monday. Kershaw’s completed eight innings or more 12 times this season.

“It’s a healthy competition. There’s no jealousy, there’s no envy,” Dodgers catcher A.J. Ellis said. “But these are two of the more competitive guys I’ve ever caught.

“They see each other and the way they’re throwing the ball. I’m sure Clayton’s No. 1 job is thinking about winning the game [Tuesday]. But deep down there’s also that thought, ‘Hey, Zack put up a pretty solid 8 2/3. Maybe I can match that.’"

For his part, Greinke has always downplayed the competition. Kershaw is in another league, Greinke says, and he’s just doing his best to keep up. Coming from a former Cy Young winner, that’s quite a statement.

“It’s not much of a challenge right now,” Greinke said of competing with Kershaw. “He’s winning pretty bad.”

Ellis thinks there’s a little more to it, though. A benefit Greinke couldn’t have anticipated this winter when he chose to sign a six-year, $147 million contract with the Dodgers. Kershaw would be there to push him, but he’d also be there to shield him.

“I think Clayton takes some of the attention away from him, which Zack doesn’t really crave, and Clayton can handle,” Ellis said.

After a slow start out of the gates in spring training, and further setback when he broke his collarbone in a brawl with San Diego’s Carlos Quentin, Greinke -- who has battled social anxiety disorder in the past -- seems more comfortable than perhaps at any point during his career.

More comfortable in the clubhouse, more comfortable with the media, and definitely more comfortable on the mound.

Monday night he even heard his name chanted by 40,965 fans at Dodger Stadium as they rooted him on in the top of the ninth, after he’d talked Dodgers manager Don Mattingly into letting him try to close out his second shutout of the season.

He wasn’t able to do it. Anthony Rizzo doubled to right center with two outs, Nate Schierholtz was hit by a pitch and Brian Bogusevic knocked in two runs with a double to left to finally chase Greinke. But the fact he felt comfortable enough with Mattingly to push for the opportunity to finish it out says a lot.

“I’m glad I got the opportunity. I’ve been talking to him over the last month, trying to get deeper into games,” Greinke said of his conversations with Mattingly. “A lot of times I’ve felt like I’ve been able to go maybe one more inning. And that’s kind of what you want to do as a pitcher, throw as much as possible.

“If you don’t do it, you don’t know what it feels like. So you have to do it, or else you forget how to.”

Mattingly responded to that competitive spirit by letting Greinke throw a season-high 122 pitches in an effort to close out the Cubs, and push for that shutout. He didn’t get it, but Mattingly liked the sentiment.

“He’d earned the right to try and finish it,” Mattingly said. “I know he wanted to.”

After two straight losses to the Boston Red Sox over the weekend, Mattingly had laid into his team before the game. One player involved said he wasn’t yelling, so much as giving them a strongly worded kick in the pants not to rest on their laurels after going 30-7 since the All-Star break.

“Donnie never really yells,” the player said. “He just wanted us to keep pushing. To know that we can’t rest.”

With Kershaw pushing Greinke, and Greinke pushing Kershaw, that won’t be an issue for the pitching staff.