The 6-foot-7 Clark drove a 96 mph fastball over the center-field fence to help San Diego extend its season-high winning streak to five games.
"I have enough of a history to know that he's a handful," Clark said. "He's throwing mid-to-high 90s [mph]. You simply try to get the bat head over the ball and take your chances from there."
The go-ahead shot sent the staggering Mets (30-32) home after a 2-5 trip to California. New York has a day off Monday before opening a six-game homestand against NL West-leading Arizona. The Mets, a World Series favorite before the season, are fourth in the NL East, 7 1/2 games behind first-place Philadelphia.
"I don't know what to say," manager Willie Randolph said. "I'm not usually at a loss for words, but what do you say? We finally score some runs and Billy's been pitching lights-out. It's frustrating."
The Padres, who have won eight of 11 overall, had their record-setting streak of 2-1 wins snapped. San Diego became the first team in major league history to win four straight 2-1 games on Saturday night, according to the Elias Sports Bureau.
The victory Sunday gave San Diego its first four-game sweep of the Mets at home since 1980.
The pinch-hit homer was the 11th of Clark's career and first with the Padres. Clark, a San Diego high school star, signed as a free agent in the offseason.
"I was trying to keep the ball down, not elevated," Wagner said. "He put a pretty good swing on it."
It was Wagner's third blown save in 16 chances. When he entered the game, Wagner (0-1) had allowed only one earned run all season.
Clark is batting .286 as a pinch hitter (10-for-35), but he had just three RBIs before the home run.
"Finally, I made a contribution other than shaking hands at the end of the game," he said.
Padres closer Trevor Hoffman, who was warming up in the San Diego bullpen in left-center, initially didn't think Clark's drive would carry over the fence.
"But once it got about 20 feet over second, it just kind of kicked into another gear," Hoffman said. "I put my head down and started throwing."
Carlos Guevara (1-0) pitched a perfect eighth for his first major league win. Hoffman worked the ninth for his 14th save in 17 chances.
Clark's homer, San Diego's first pinch-hit home run of the season, deprived a shaky Pedro Martinez of his second win since he returned from the disabled list Tuesday.
"I thought I had better command even though the results weren't as good," he said. "I battled my way through but they made contact."
Martinez lasted just five innings. The three-time Cy Young Award winner had been out of action since April 1 with a strained left hamstring before coming off the DL on Tuesday and winning at San Francisco.
He labored through a three-run first inning when he gave up four singles, hit a batter with a pitch and balked in a run. Martinez settled down but left after 97 pitches. He allowed four runs and 10 singles with four strikeouts and no walks.
Wagner relieved Duaner Sanchez with two outs in the eighth and runners on first and second. The left-hander gave up an RBI single to Jody Gerut that cut New York's lead to 6-5. Gerut, who had three hits, also drove in a run with a single in the fourth.
"It was a slider that I tried to take it off the plate and hung it," Wagner said. "That was the guy to get out so I wouldn't have to face [Clark]."
Right fielder Endy Chavez threw out a runner at third base and robbed Adrian Gonzalez of a hit with a diving catch. Chavez also had two hits and an RBI on a bunt single in the seventh that put the Mets up 6-4.
New York scored three runs in the first, equaling the number of runs it scored in the first three games of the series. Damion Easley had a two-out RBI single and Delgado hit a two-run triple into the right-field corner.
The Padres answered with three runs in the bottom half, scoring first on a balk by Martinez with the bases loaded. Paul McAnulty then blooped a two-run single that tied the score at 3.
Delgado's two RBIs gave him 1,403, one behind the leader among players from Puerto Rico, Juan Gonzalez. ... The Mets became the sixth team in major league history to lose three straight 2-1 games with Saturday night's loss to the Padres. The last team to do so was the 1991 Milwaukee Brewers.