Nyjer Morgan had two hits and reached base five times for the slumping Pirates, who have lost six straight and 10 of 11 overall.
Pittsburgh also has lost six consecutive road games.
Jose Reyes got the winning rally started with a single to center off Tyler Yates (0-2). Luis Castillo then walked before Beltran sliced a single down the third-base line to give New York a 3-2 lead.
Sean Burnett came in for Yates and Delgado greeted him with a drive over the wall in right-center. Delgado's fourth homer gave him 1,512 RBIs, snapping a tie with Mickey Mantle for 48th place on the career list.
Omir Santos tacked on an RBI single as New York sent 11 batters to the plate in its second-biggest inning of the season. The Mets scored six runs in the first against Florida on April 27.
Bobby Parnell (1-0) struck out two in a perfect eighth to earn the win.
New York got a big lift from Niese, who gave up two runs and seven hits. Niese was recalled from Triple-A Buffalo when struggling left-hander Oliver Perez went on the disabled list Wednesday with tendinitis in his right knee. Reliever Ken Takahashi was slated to take Perez's turn in the rotation but the Mets instead opted to give Niese his first start of the season.
Niese got a break in the first when Morgan slid past second on a steal attempt and was tagged out before Nate McLouth's base hit into left field. Morgan pounded the bench when he got back to the dugout.
But Niese experienced a little misfortune in the third. Morgan hit a one-out RBI single and moved to second on Freddy Sanchez's groundout. McLouth then hit a lazy fly that looked like the final out of the inning.
Beltran, a Gold Glove center fielder, and right fielder Ryan Church each ran into right-center to get the ball but it landed behind Beltran in center. Morgan scampered home on McLouth's double to tie it at 2.
Pirates right-hander Jeff Karstens also had to deal with some bad luck. Castillo's well-placed grounder to the right of the mound in the first helped set up Delgado's two-run single.
Karstens allowed two runs and seven hits in six innings after going 0-1 with an 8.10 ERA in his previous two starts.
Notes: Pirates SS Jack Wilson (sprained left middle finger) was scheduled to begin a rehab assignment with Triple-A Indianapolis on Friday night. ... Mets RHP John Maine, who turned 28 on Friday, is scheduled to start the second game of the series against LHP Paul Maholm. ... With the lefty Maholm on the mound, Mets manager Jerry Manuel said OFs Gary Sheffield and Fernando Tatis will start Saturday. ... Manuel tweaked his lineup for the opener of the weekend series. 2B Castillo batted in the second slot for the sixth time this season and LF Daniel Murphy was in the six-hole for the second time. Church batted eighth for the first time since Oct. 1, 2006, for Washington against the Mets, according to the Elias Sports Bureau. ... Church went 1 for 4 and is 4 for 34 over his last 11 games. ... The Pirates announced that RHP Jimmy Barthmaier will have reconstructive surgery on his right elbow on Tuesday. The surgery will be performed by Dr. James Andrews in Birmingham, Ala.
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