Curtis Granderson hit a tying triple for the Mets immediately after Kershaw was lifted with two outs in the eighth. But the Dodgers quickly regrouped for their sixth victory in seven games since losing four straight.
"There's no emotional letdown," Gonzalez said. "It's a tie game. First team to score for the most part is going to win that game. So that was our mentality."
Los Angeles took two of three at Citi Field before a trio of sellout crowds on a weekend when the NL champion Mets celebrated the 30th anniversary of their 1986 World Series crown.
The Dodgers won the season series 4-3 after New York captured a tense, five-game playoff between the teams in October.
"There were some fortunate things that happened obviously tonight, but, take it," Kershaw said. "Just celebrate tonight. We beat the Mets."
Kershaw struck out 10, walked none and capped a magnificent May with another sublime performance. He was in position to win his sixth consecutive start when manager Dave Roberts made a double-switch with a runner on first in the eighth, pulling Kershaw after 114 pitches.
The three-time Cy Young Award winner and 2014 NL MVP didn't look happy about it, handing the ball to Roberts and briskly walking off the mound without appearing to make much eye contact.
"It's a tough situation. That's why I'm not the manager," Kershaw said. "I think managers appreciate when you don't want to come out of the game and obviously I didn't want to and never really do. But you know what? He's making the decisions and you've just got to respect it."
Roberts went to lefty Adam Liberatore, who had limited left-handed batters to a .107 average this season (3 for 28). But the move backfired when Granderson hit an RBI triple to the right-field fence over a leaping Yasiel Puig.
"I made the decision and I've got to live with it," Roberts said. "I believe in the other guys, too."
Liberatore (1-0) struck out Asdrubal Cabrera, who homered earlier off Kershaw, to end the inning.
Familia blew a four-run lead in the ninth inning of the series opener only to get bailed out by Granderson's game-winning homer. This time, the reliever wasn't so fortunate.
"He's one of the best in baseball. This is very uncharacteristic of him ever since he's taken over the closing job. So we're in as big a shock as anybody," Mets manager Terry Collins said.
Familia (2-1) allowed more runs in the Dodgers series (six) than he previously had all season (five).
Kenley Jansen worked a perfect ninth for his 15th save in 17 chances.
Gonzalez had an RBI single and Justin Turner drove in Chase Utley with a groundout to help the Dodgers build a 2-0 lead against Bartolo Colon, who pitched six solid innings in his first outing since his 43rd birthday.
Kershaw yielded four hits and finished 5-0 with a 0.91 ERA in six May starts. He had 65 strikeouts and two walks during the month. The left-hander leads the majors with 105 strikeouts and has walked only five. That's the best ratio for any major league pitcher when he reached 100 strikeouts in a season, according to the Elias Sports Bureau.
Dodgers: LHP Hyun-Jin Ryu (shoulder surgery) woke up with shoulder soreness after his most recent rehab outing with Triple-A Oklahoma City and will probably skip a turn, Roberts said. He could still be two rehab starts from rejoining the Dodgers. ... RHP Kenta Maeda should be fine to make his next scheduled start Thursday against the Cubs after getting hit in the pitching hand by a line drive Saturday that did not knock him out of the game. X-rays were negative and the swelling went down. ... OF Trayce Thompson, who left Saturday's game with lower back soreness, was 100 percent and available off the bench, according to Roberts. ... RHP Brandon McCarthy (Tommy John surgery) will face hitters Monday.
Dodgers: LHP Alex Wood (1-3, 4.03 ERA) starts Monday afternoon against RHP Jason Hammel (6-1, 2.17) and the major league-leading Chicago Cubs at Wrigley Field. Wood's turn was pushed back three days due to a sore left triceps. In his most recent outing, he struck out a career-high 13 and walked one in six innings at San Diego.
Mets: RHP Matt Harvey (3-7, 6.08 ERA) tries again to get back on track when he faces the skidding White Sox in a Memorial Day matinee at Citi Field, weather permitting. AL ERA leader Jose Quintana (5-4, 2.22) pitches for Chicago, which has dropped six straight and 14 of 18.
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