This Is How Close Jay-Z Came to Canceling Last Yankee Stadium Show

One hour after Jay-Z was supposed to be onstage Sunday night, almost half the Yankee Stadium crowd was still stuck outside the venue ... creating 3 hours of chaos behind the scenes for Jay, his superstar guests, NYPD, and fans.

Sources smack in the middle of the situation tell TMZ ... the first sign of trouble came at 8:55 PM. Mind you, Jay had been hitting the stage around 9 PM for the first two Stadium shows, but when a few hundred people without tickets bum-rushed an entrance -- some actually got in -- security shut down ALL gates, and no one was allowed in or out.

At 10:15 PM, we're told there were still 20,000 fans lined up outside the Stadium ... and even A-listers like A$AP Rocky, Tyler the Creator, and Usher -- who were scheduled to perform -- were locked out. Our sources say NYPD was adamant no one was getting in, and they didn't even bend when members of Jay's team tried to get the VIP guests inside.

We're told there were discussions about canceling the show, but Jay didn't want to do that because so many fans had traveled from out-of-state, and it would be nearly impossible to reschedule for a new date at the Stadium.

Our sources say it took a meeting between NYPD brass at the stadium, Yankees top executives and Jay's RocNation team before cops approved opening a single gate, at first, and then slowly opened up others ... allowing the masses to trickle inside.

Now, at 11 PM, we're told there were STILL about 10,000 fans outside, and it was suggested Jay should just start the show -- 2 hours late is better than no show, after all -- but that also didn't sit right with Hov. All the people outside had paid good money, and ultimately, he didn't want to screw them over ... according to our sources.

Of course, there was also the potential for triggering a stampede to consider. What would those 10,000 people do when they suddenly heard the music??

Weighing all those factors, Jay-Z and his legion of guest stars -- including Beyoncé, Rihanna, Pharrell Williams, Fat Joe, and Jeezy -- decided to just sit patiently backstage.

Memphis Bleek told us Jay was stone-faced through the delay, but determined to perform.

Finally, at midnight -- when the team decided the crowd outside was small enough -- they made the call to get ready to hit the stage, and 50 songs later, around 3 AM, the show ended with a massive fireworks display.