Martinez (4-0) allowed just one run and two hits and reached double digits in strikeouts for the 105th time in his career.
"I am glad that I do not have to face him any more," Delgado said. "I think I have faced him probably 80 to 85 times in my career so it is a nice break."
Martinez did not allow San Diego to put together any threats and has a 3.04 ERA in 26 2/3 innings this season. He became the first Mets pitcher to go 4-0 to start the season since Frank Viola started 7-0 in 1990.
"I had pretty good command today," Martinez said. "I got ahead with the fastball a lot. After I was ahead I was able to mix in some cutters and the breaking ball came back whenever I needed it."
The 6-foot-10 right-hander worked four innings, allowing six hits and four runs. The Mets had been held to one run in three of their last four games.
Mike Piazza led off the bottom of the second by hitting a 429-foot homer to left against Martinez, a former Mets teammate. The homer was Piazza's 399th, and first since he connected on opening day in his first at-bat with the Padres.
"At 2-0 I wanted to throw a strike, I wanted to get him. It was a cutter," Martinez said of Piazza's at-bat. "But Mike didn't waste any time and he does really well against me in his career."
New York had a chance to blow the game open in the third, as Delgado led off with a walk, David Wright singled and Cliff Floyd was hit by a pitch. Nady hit into a double play to score a run and Castro followed with a two-out, RBI single to give New York a 4-1 lead.
Young, who had allowed just one run in winning his last two starts, was replaced in the fifth by Dewon Brazelton with two on and no outs. Brazelton pitched out of that jam, but Delgado to led off the seventh with his eighth homer to make it 5-1.
Afterwards, Young said he has been pitching with a thumb injury since his first start of the season. Young said he jammed his thumb during batting practice before his first start.
"There is no pain, just coldness which leads to a lack of sensation," Young said. "It feels like I stuck my thumb in a freezer."
Young is scheduled to see a hand specialist on Monday.
Delgado also walked three times and was hit by a pitch, to go along with the homer.
"I don't try to hit home runs," Delgado said. "When you come to a big ballpark you just want to hit the ball hard somewhere and if it goes I'll take it."
Floyd also had a sacrifice fly in the seventh to extend the lead to 6-1.
Jorge Julio followed Martinez with two scoreless innings to complete the combined three-hitter.
"Pedro was tough," San Diego's Brian Giles said. "He was throwing as well as I've seen him. He mixes it up so well, he makes it tough to get comfortable up there against him."
- Delgado's homer was the 377th of his career, which ties him for 57th on the career list with Norm Cash. Delgado's eight homers in April is one home run shy of tying Dave Kingman's franchise record for homers in April in 1976.
- Piazza had gone 7-for-41 (.171) since opening day before the homer off Martinez.
- Castro had four hits.