Kennedy earned his first victory in more than two months and Cabrera had two hits and two RBIs as the Padres beat the New York Yankees 6-3 on Sunday.
The Padres took two of three from the Yankees, who got only 2 2/3 innings out of Phil Hughes.
"The adrenaline got the best of me later on, but early on I started feeling it, trying to control it," Kennedy said. "A lot of things going on. First start, against the team that drafted me, it was a lot into it, coming over here. I got the first one out of the way and the offense carried me."
Kennedy (4-8) was taken by the Yankees in the first round of the June 2006 draft. He was traded to Arizona in December 2009.
That was it for Kennedy, who allowed two runs and four hits in 5 2/3 innings, struck out six and walked four.
Manager Bud Black said he thought Kennedy pitched well.
"Anytime you come to a new team there's emotion and there's quite a bit of adrenaline, and I think at the end he sort of ran out of it a little bit. I think he tired a little bit quicker than what you'll see in the future. I think that's what happened there in the sixth inning.
"Again, for him, it's been three days of a lot of emotions, getting traded and coming to a new club," Black said. "I thought he handled it well. I liked what I saw. I told him that's going to be one of many wins for the Padres."
Kennedy said he welcomed the fresh start.
"Coming here, within the division is a little bit different because I've faced these guys I don't know how many times over the years," Kennedy said. "But you get a different perspective from the pitching coach, or video guys, the manager, just a little different. I like it."
Cabrera, the Padres' All-Star shortstop, is among 14 players facing discipline in the Biogenesis of America anti-aging clinic. Major League Baseball appears poised to levy suspensions Monday.
Yankees All-Star third baseman Alex Rodriguez is another of the players set to face discipline. Major League Baseball has informed New York that Rodriguez will be suspended Monday in the Biogenesis drug case, but can play while he appeals the penalty, a person familiar with deliberations told The Associated Press on Sunday. The person spoke on condition of anonymity because no announcement was authorized.
"I want him back with us. This is arguably one of the best hitters of all-time," Granderson said. "Having him in the lineup is obviously going to be very positive for us."
Rodriguez is set to make his season debut when the Yankees play the Chicago White Sox.
Cabrera singled in two runs with two outs in the three-run second before getting thrown out trying to steal second. He leads the NL and is second in the majors with 37 steals.
Huston Street pitched the ninth for his 21st save in 22 chances.
Hughes (4-10) had his second-shortest outing of the season, allowing five runs and six hits while striking out one and walking one.
"He couldn't put people away," manager Joe Girardi said. "The bottom line is, he didn't make pitches when he had to."
Hughes, who's 0-3 in his last five starts, agreed.
"I blew an opportunity there in the second to get an out, two outs, and it comes down to not making quality pitches when I had to," he said. "There were runners in scoring position and a lot of long counts and just a battle the entire time. Unfortunately, I wasn't able to execute a couple of big pitches with two outs."
The Southern California native got through the first inning unscathed but was roughed up in the second and third innings. He allowed singles to Will Venable and Chris Denorfia opening the second before Mark Kotsay hit a sacrifice fly. He then walked Nick Hundley before Kennedy sacrificed ahead of Cabrera's two-run single.
Hughes again put on the first two batters in the third, allowing a single to Amarista and walking Headley, and again, both scored. Denorfia hit a sacrifice fly and Kotsay hit an RBI single with two outs.
The Yankees are a season-worst 9½ games out of first place in the AL East and 4½ out in the race for the second wild-card spot.
An MRI exam revealed that Yankees SS Derek Jeter has a strained right calf. He sat out Saturday and Sunday, and the Yankees hope to know more about his condition on Monday. ... The Yankees open a three-game series at the Chicago White Sox on Monday night, with LHP Andy Pettitte (7-8, 4.28) scheduled to oppose LHP Jose Quintana (5-3, 3.62). ... The Padres are off Monday before opening a two-game series against the Baltimore Orioles. Tuesday's scheduled starters are Baltimore RHP Bud Norris (7-9, 3.89 ERA) against San Diego RHP Edinson Volquez (8-8, 5.56).
Information from The Associated Press was used in this report.