This marked the 10th time in the last 11 games that the Pirates have been held to two or fewer runs, though this is the first time that such minimal run support still produced a win.
"It's good to see a well-pitched game and actually win one," manager John Russell said. "We played an all-around good game."
Duke, who entered the game winless in August, allowed a first-inning run before shutting down the Mets through his final six innings of work. He allowed just five hits, walked two and struck out five.
Key, too, was the fact that the lefty was finally able to avoid succumbing to the big inning.
"I really felt from the first inning on my location was good with all my pitches and I was able to mix them up," Duke said. "The fact that I was able to bounce back after the run in the first inning really got the momentum in our favor.
"Then those two home runs were just huge for us," he added. "Thankfully we were able to get the win that we needed."
The first of those two came from Lastings Milledge, who had started just one of the previous six games. Milledge had been relegated to a part-time role after the Pirates' decision to get Ryan Doumit more playing time in right.
Still, Milledge had hit safely in each of his last 11 starts. And he extended that streak to a dozen in the fifth, when he teed off on Santana's two-out, 0-1 changeup.
The solo home run tied the game at 1.
"He stays focused, even on the bench," Russell said. "He will get his chances. The good thing about Lastings is he stays ready. No hanging his head. He's ready to compete every day."
The Pirates collected only three other hits, two of which were singles by third baseman Pedro Alvarez -- the first giving the Bucs their first hit in the fifth inning. The other -- a solo shot by Tabata -- stuck as the game-winner.
For Tabata, the hit was especially meaningful. The Venezuelan native, knowing that Sunday's game was going to be televised in his home country, had talked to his mother early on Sunday to deliver a promise.
"I told her everyone in Venezuela will be watching the game, and I want you to see the game because I'll do something special for you, Mom," Tabata recalled saying. "And thank God for the home run."
That blast, which also came with two outs, traveled over the left-field wall in the sixth.
Minutes after the game, Tabata had already received a call from his mother.
"She was so happy, like, 'Wow, my son hit the home run,'" Tabata said. "She said, 'You told me you'd do something -- not the home run, but something -- and thank you God, hit the home run.'"
Though Santana went on to pitch his third consecutive complete game, those two solo home runs were enough to drop his record to 10-8.
"It seemed that everything was working out pretty good and a couple mistakes, a couple pitches, changed the whole ballgame," he said.
The win -- Pittsburgh's fifth all month -- was sealed with scoreless innings of relief from Evan Meek and Joel Hanrahan. Hanrahan allowed a leadoff single in the ninth, but secured his second save of the season by following with three routine outs.
"That's what we like to see from those guys," Russell said. "We feel pretty good when we have a lead in the eighth."
Jenifer Langosch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.