Cole (6-2) gave up just six hits -- all singles -- and walked one to lower his ERA to 2.05 as the Pirates won for just the second time in their last eight games. Mark Melancon got the final two outs for his 10th save.
Syndergaard (1-2) struck out the first four batters he faced and fanned five in all but surrendered four runs, three earned, in six innings. Juan Lagares reached base twice and scored New York's only run on a wild pitch.
The scuffling Pirates have relied heavily on Cole to become the stopper during an uneven opening quarter of the season. The 24-year-old halted Pittsburgh's latest slide with his longest start of the season, keeping the Mets off balance with a fastball that topped out at 99 mph and a rapidly improving breaking ball. His defense chipped in whenever the Mets appeared ready to mount a threat, turning four double plays. Stewart also threw out two runners trying to steal second base, boosting Pittsburgh's caught stealing total to 20, the best in the majors.
Syndergaard kept pace early but allowed the bottom of the Pittsburgh lineup to peck away at him in his third career start. He struck out the side in the first before the Pirates started to time up a fastball that reaches the upper 90s. Alvarez doubled with two outs in the second and scored when Polanco snapped an 0 for 19 slump with an RBI-single to right.
Lagares pulled the Mets within a run in the third when he reached on an error and came around to score when a Cole curveball skipped away.
Syndergaard tired in the sixth, just as he had in each of his first two starts. His defense didn't help. Andrew McCutchen led off the inning with a double and scored on Kang's single. Kang moved to second when a pickoff attempt sailed wide of first and New York first baseman Lucas Duda declined to throw to second even though he appeared to have plenty of time. Kang swiped third without a throw when the Mets decided not to cover the bag and scored with an unorthodox but effective slide on a sacrifice fly by Alvarez.
That was more than enough for Cole, who came within two outs of Pittsburgh's first complete game since July 28, 2014.
Mets: RHP Dillon Gee will rejoin the team on Saturday and could give New York a six-man rotation. Gee is on the 15-day disabled list with groin discomfort. 3B David Murphy and C Travis d'Arnaud both took live batting practice on Friday as they continue their rehab from various injuries.
Pirates: RHP Charlie Morton will return to the starting rotation Monday when Pittsburgh begins a three-game series with Miami. Morton hasn't started a game in the majors since last September. He underwent offseason hip surgery and the rehab took longer than expected. He is coming off a solid start for Triple-A Indianapolis on Tuesday. Vance Worley (2-3, 4.17 ERA) will move the bullpen as a long reliever.
The three-game set continues on Saturday with a prime pitching matchup as New York's Matt Harvey (5-1, 1.98 ERA) faces Pittsburgh's resurgent A.J. Burnett (3-1, 1.38). The 38-year-old Burnett is second in the majors in ERA and is coming off seven scoreless innings in a win over the Cubs last Sunday. Harvey has not given up a run in his 16 innings while becoming the fifth pitcher in team history to surrender no runs with nine strikeouts in consecutive starts.