LOS ANGELES -- All roads heading up to Dodger Stadium on Tuesday led directly to Rich Hill.

The savvy veteran, in the midst of a career rebirth at age 36, had what he called his finest game ever, considering the circumstances. In the process, his 12 years in the major leagues came full circle in one night, with a curvature that felt like one of his round-house breaking balls.

The former Chicago Cubs product, who probably thought he might help his former team break their multiple-generation curse one day, is living by a different credo now. Currently with the Los Angeles Dodgers, his brilliant six innings in Game 3 of the National League Championship Series might help extend that curse even further.

The Dodgers' convincing 6-0 victory gave them a 2-1 lead in the series, a slight edge that is hardly commanding, but every day the pitching staff holds the Cubs' dynamic offense without a run, the more the momentum builds in Southern California. The Cubs were held without a run for the second consecutive NLCS game.

It is implausible that Hill would have been the guy anybody would have pegged as a key member of a playoff rotation, and especially not a year ago at this time when he was barely out of a stint in independent baseball.

Freed last summer from his commitment as a minor league pitcher with the Washington Nationals organization, Hill could not find a taker for his relief-pitching services. So he hooked up with the Long Island Ducks, moving back into the starting role he had for a few seasons with the Cubs (2005-08), and one more with the Baltimore Orioles in 2009.

He had been a reliever since that 2009 season, and if somebody would have predicted that seven years after moving to the bullpen he would be knocking out six scoreless innings to move his team two victories away from the World Series, the skeptic would have laughed. But why not? This is the year the Cubs had the best record in baseball after all.

Hill so dazzled in his short stint at Long Island that the Boston Red Sox signed him to join the starting rotation for the rest of last season. This past offseason the Oakland Athletics offered him a $6 million contract to start for them. Hill did, and he pitched well, but in spring training, it was still hard to see the left-hander making this kind of impact.

Josh Reddick is the one Dodgers player who has watched Hill's entire season play out, first in Oakland and now with the Dodgers after an Aug. 1 trade. Reddick said this day looked dubious seven months ago.

"In spring training, he was a completely different guy," Reddick said. "We were playing behind him, and he couldn't find the strike zone. He was struggling a little bit there. Then, ever since start No. 2 of the season, he's been one of the better pitchers in baseball. So for him to make that adjustment, it has been huge for us, and it's been great to come over with him and see him continue that success."

It all starts and ends with Hill's curveball, a slow tantalizing pitch than bends aggressively from top to bottom. When it is on, the way it was Sept. 10 at Miami when Hill pitched seven perfect innings, it is a thing of beauty. When it is off, and dragging down his efficiency, things like his 2 2/3-inning start in the deciding game of the National League Division Series happen.

But the Dodgers managed to win that game to move on to the NLCS, giving Hill the chance at redemption he put together Tuesday.

His only blemish on an otherwise dominating night was a shaky 30-pitch second inning when he walked two batters and ran into a second-and-third situation when a passed ball got through catcher Yasmani Grandal.

But Hill extricated himself from a jam of his own doing, striking out the struggling Addison Russell, and retiring Cubs' Game 1 hero Miguel Montero on a ground out. With the hard part out of the way, Hill cruised.

"[Grandal] did a great job of getting me back on track," Hill said. "I was just executing pitches after that. Just getting back to executing pitches one pitch at a time, that was it. Don't think about the two walks or the outcomes of those two walks."

What was Grandal's secret to changing his pitcher's fortunes? Trust.

"Once his curveball is missing for strikes, you can't really think about it, that's his go-to pitch; everybody knows it," Grandal said. "It's like Kenley [Jansen], you know? He's throwing that cutter. If you can hit it, you can hit it. So we were going to live or die with his best pitch."

When that pitch returned, so did Hill's quirky bunny-hop. The left-hander employs so much body English at times that his follow-through includes a bounce off the mound. It was present often Tuesday, and it was a pleasant sight for his teammates.

"When he's got that attitude out there, that's when you can tell," first baseman Adrian Gonzalez said. "That's when you know he's rolling, and his pitches are working, and he's doing what he wants to do out there. You saw him stress a little bit in the second, but once he got out of that second, it was cruising from there, and he did a great job."

Relievers Joe Blanton, Grant Dayton and Jansen finished off the shutout, with Jansen recording the final four outs in a non-save situation. It gave the NLCS victory to Hill, something that would have been hard to predict a year ago.

If Hill's career arc were a bridge, there would be dangerous gaps in the roadway. But the surface is smooth now, and Hill is enjoying the ride.

"It's the biggest game of my career, and it's all about staying in the moment and executing when you're in that moment, and that's all you can think about," Hill said. "And that's all you can control is that pitch. In the second inning, walk a few guys, it's over with, you can't control it, and you move on. You execute the next pitch, and you execute the pitch after that. And you continue to execute until the ball gets taken out of your hand."

It was nearly taken out of his hand for good a year ago. But Hill has persevered and his confidence seems fully elevated.

"For me, looking back and getting to this point, it's just putting in the work, putting in the time, having a routine, persevere, all those things that you can kind of say to sum up some kind of endurance or resiliency," Hill said. "For me, that's all I've ever known, is just work and just continue to do the work."