Fifty years ago this week marked the turning point in the Mets’ miracle World Series run. It was the night the Mets’ future Hall of Fame pitcher, Tom Seaver, pitched his “imperfect game,” giving up just one base hit in the ninth after retiring the first 25 batters of the opposing team.

Playing in their eighth season, the Mets were winning for the first time in the team’s otherwise hapless history up to that point. In 1969, the team finally arrived, and New Yorkers took notice.

During the second week in July, the first-place Chicago Cubs, the team to beat in the National League Eastern Division, came to Shea Stadium.

The Mets won the first of this three-game series. Game two, on July 9, 1969, saw thousands of fans show up to form long lines at the stadium ticket booths. Some 59,000 fans were admitted — still the largest home crowd that ever attended a Mets game. (Shea had a seating capacity of little more than 55,000.)

Among those in attendance were my mother, grandmother and three older brothers, having traveled over the backed-up Whitestone Bridge (long before E-ZPass) in our ’66 green Volkswagen bus. “We ended up sitting in general admission, about 10 rows from the top, on the steps,” my brother Mike recalled. “From the very first batter, Seaver was electric. You knew he was going to have a good night.”

After the Mets’ first seven losing seasons, when they finished in last place or second to last, the team was given 100-to-1 odds for winning the World Series in 1969. Starting out that season, they continued with more of the same by losing seven of their first 10 games. Around Memorial Day, the team was five games under .500 and nine games back from first place.

Then things changed. Beginning in the last week in May, the Mets went on an unprecedented 11-game winning streak, hitting the .500 mark on June 2.

By the time the Cubs showed up at Shea in July, the Mets were 11 games over .500 and in second place in the Eastern Division, 3 ½ games behind Chicago.

“These were the first ‘big games’ the Mets ever played in their history,” Seaver reminisced years later.

Led by their famous manager, Leo Durocher, the Cubs had a formidable lineup that included future Hall of Famers Ernie Banks and Billy Williams. The Mets’ pitching ace humbled them all night long.

Excitement had been building, especially by the seventh-inning stretch — nobody from the Cubs “had been on base,” another brother, Tim, recounted. Seaver was pitching a perfect game — baseball’s most rare achievement.

Taking a 4-0 lead into the ninth inning, he retired the first batter. Then the next, Jimmy Qualls, hit a clean single to left field. “Everyone was standing, and after that hit, we all sat down to take a breath; then we stood up again and cheered him for such phenomenal pitching,” Tim recounted. Seaver got the ­final two outs to complete a one-hit shutout.

Incidentally, Qualls’ notorious single that night was one of only 31 hits in his ephemeral three-year Major League career.

By Sept. 10, the Mets would overtake the Cubs for first place in the division — one day following another series with Chicago at Shea — and they never looked back. My mom and four of my older siblings also attended that second of two games, when Seaver prevailed against another future Hall of Fame pitcher, Cubs ace Ferguson Jenkins.

“Fans were buying Cub pennants and lighting them on fire in the stands,” my brother Mike recalled. “On the way out of the stadium, walking down the ramps, thousands of fans were chanting in unison, ‘We’re No. 1!’ ” For the Mets’ early history, this was unimaginable.

The Mets, of course, would go on to win the Eastern Division, sweep Hank Aaron’s Atlanta Braves in the National League Championship Series and defeat the heavily favored Baltimore Orioles in the World Series by four games to one.

Half a century ago, the Mets franchise was transformed by its greatest player, Tom Seaver, and the team’s historic ’69 season would go down in baseball — and New York — history.

Peter Murphy grew up in Westchester County and is a lifelong Mets fan thanks to his late mother, Jean. Twitter: @PeterMurphy26