"Everybody is healthy and everybody is feeling good," Kemp said. "We're definitely confident in the things we can do and hopefully we are that last team standing at the end of the season."
The team remains a half-game behind San Francisco in the National League West but now stands 2 1/2 games ahead of third-place Arizona with the victory.
The Dodgers are 9-6 in their last 15 games and they are starting to resemble the sort of club management hoped it would when it began making deals left and right around the Trade Deadline.
"I know we had the little series hiccup there with Arizona, but we just came off a trip where we were basically 7-3 and we swept San Francisco there," manager Don Mattingly said. "One little series is not going to change my mind."
While the entire team has rebounded, so has Kershaw, who gave up eight runs in 5 2/3 innings against St. Louis on July 27.
Since then, he has thrown a shutout against the Giants, and he looked sharp on Saturday against a Cubs team that entered this three-game series 19-12 in their last 31 games.
"He's been the same all year, honestly," Mattingly said. "He's been good. This kid is good all the time. I talked about it in Spring Training -- there's going to be games where he can pitch just as good as last year and not get wins."
On Saturday, that wasn't the case as the lineup was able to give him just enough run support to earn his ninth victory of the season.
The Dodgers have now taken the first two games of the series and look for a sweep with newly acquired Joe Blanton making his debut on Sunday.
"We win tonight and we win a series tonight," Mattingly said. " ... Hopefully we get greedy tomorrow and come out ready to play."
Kershaw surprisingly needed to be at his best on Saturday despite facing Chris Volstad, who was 0-7 with a 7.94 ERA and winless in his previous 20 starts dating to last season.
Volstad allowed only two runs on six hits and proved to be a formidable foe for Kershaw by throwing seven strong innings of his own.
"It's unfortunate [Volstad] had to be matched up against last year's Cy Young winner and a guy who is throwing the heck out of the ball this year," Chicago manager Dale Sveum said. "[Volstad] matched him pitch for pitch and it was a good game and unfortunate we couldn't muster any runs."
Kemp's home run off him in the fourth proved to be all the Dodgers would need to guarantee an L.A. series win.
Mark Ellis led off the bottom of the frame with a single into right field and Kemp followed it up with a shot to right field that bounced in and out of the glove of a leaping Joe Mather to give the Dodgers and Kershaw a 2-1 lead. It was Kemp's team-leading 16th home run of the season.
"You never know in this ballpark," Kemp said. "It's tough to hit home runs at night here and I think I got a little bit of help looking at the Jumbotron."
Alfonso Soriano hit an RBI double in the top half of the inning that scored Darwin Barney, who reached on a single and advanced to second on a groundout.
The Dodgers added an insurance run in the eighth when Shane Victorino, who led off the inning with a double, scored on a ground ball hit by Hanley Ramirez that slipped past the glove of shortstop Starlin Castro.
Ronald Belisario and Kenley Jansen took over for Kershaw and shut the Cubs down in the eighth and ninth innings to wrap up the win as this week's punchless showing against the D-backs appears out of mind.
"Arizona was a tough series," Kershaw said. "I don't know if it was a wake-up call, but we had to play better than we did."