Using technology from these internet giants, thousands of football fans were able to watch long segments of many contests free of charge during the league's Week 13 schedule of games last Thursday and Sunday.
Dozens of these video streams, pirated from CBS and NBC broadcasts, featured ads from well-known national brands interspersed with game action.
This online activity comes as the league struggles with declining ratings that have been blamed variously on player protests during the national anthem and revelations about former players suffering from a brain disease caused by concussions.
Yet this illegal distribution of NFL content may also be crimping the league's viewer numbers.
The NFL strictly controls television and online video rights to its games. In particular, games played by teams that are not in a local TV market are often not televised except on DirecTV, and only for subscribers who pay extra for a package called "Sunday Ticket." That package starts at $55 per month.
If pirated versions of these games are available online users might ignore the DirecTV package, or skip locally televised games that they might otherwise watch. It also means that advertisers are reaching audience members that they did not pay for.
Facebook reportedly is prepared to spend more than $1 billion for the rights to future sports content, but as of now Amazon is the only large technology company with a streaming deal for football. It paid $50 million for the rights to stream 10 Thursday Night Football games this year.
CNBC was able to find dozens of feeds on Facebook and YouTube (including duplicates of the same game) over the past week. Most were disabled by Facebook and YouTube after as little as 10 minutes, but some stayed online for 20 minutes or more -- long enough to attract thousands of viewers.
For the majority of games followed by CNBC (though not all) these pirated video feeds attracted more viewers on YouTube than on Facebook.
For example, with 10:32 left in the second quarter of Thursday night's game between the Washington Redskins and Dallas Cowboys, 6,986 people were watching a feed posted by a YouTube user named "Kai sisir," according to the stream's counter.
Over on Facebook, meanwhile, a stream of the same game, posted by a user called "Unlimited Stream NFL," had attracted some 2,000 viewers by the time it was shut down at 5:49 p.m. PT.
The following screen shots show some of the games that were available to watch this past Sunday.
While many of these videos were uploaded to YouTube and Facebook via feeds with names such as "Allsport live," "HQ Live," "Live Streaming NFL" and "Am_Football Live Anvivo," none were able to maintain a truly live feed. Rather, most videos trailed the action televised on the networks by at least a play or two.
And the viewing experience was far from seamless, with feeds shut down at times during an important play, as when YouTube shut down the one from Kai sisir just after Redskins quarterback Kirk Cousins fumbled the ball with roughly 9:40 left in the second quarter.
Still, a determined online viewer willing to jump from one feed to another can watch long portions of games that otherwise would be unavailable in their region or require a subscription to the Sunday Ticket.
These pirated feeds were made easier to find thanks to the search software of both companies. Typing the letters "nfl" into the search box on either website prompted the software to suggest similar, related phrases such as "nfl live streaming," for example.
Clicking on that search string then called up a list of video feeds for various games:
YouTube also hosts several tutorial videos explaining how to watch the NFL for free.
To give one measure of the interest in these pirated streams, one posted two years ago by a user called WizzyIggy had been viewed 177,000 times as of Monday afternoon.
Facebook said via a spokesperson that it uses "reference streams" provided by video publishers and media companies to check for pirated content with a tool called Rights Manager.
"If a match surfaces, Rights Manager immediately takes action on the rule set by the rights holder -- for example, to block that stream," the Facebook spokesperson said in an email. "We've been growing our global team that processes these reports across time zones and continue to invest in our copyright tools. This remains a work in progress," the email said.
An NFL spokesperson said the league was aware of the problem and have people whose full-time job is to track down illegal content and cases of piracy. YouTube did not return requests for comment.
Uploading and hosting one of these feeds can turn ordinary Facebook or YouTube users into minor social media celebrities -- although the fame is fleeting.
A Facebook user named Johnny Garcia uploaded an almost-live video feed that drew 1,400 viewers, 60 comments and 8 shares on the website.
Like owners of a digital sports speakeasy, these video pirates warn viewers that the show will end soon and alert them where to go next to keep watching.
"Sorry for the lag, I will fix when my stream gets put down, I will re-upload," Garcia said in a comment stream that ran in the stream he uploaded.
Before it was taken down with 3:25 left in the first quarter, it had been on for at least 15 minutes, long enough to show ads from national brands like Bounty, Amazon and Sprint.
A feed on YouTube uploaded by a user named "girangerwoder235" posted a message on it that said: "We Can't Broadcast Here Because YouTube copyright Click Link in comment."
It had 274 people watching when the feed was disabled.
The presence of ads -- and the quality of their feeds -- gave some pirate streams an air of legitimacy.
For example, the game between the Tennessee Titans and Houston Texans early Sunday contained a long break in play at the 10:40 mark of the second quarter as officials reviewed a 4-yard touchdown pass by Texans quarterback Tom Savage.
At that point, the CBS broadcast of the contest showed ads from Dodge, Verizon and Kay Jewelers, followed by promotional videos for the Carol Burnett 50th Anniversary Show and another for another show on the network called Man with a Plan.
A CNBC reporter watched them all on a feed called "NFL Unoficcial LIVE," with a misspelling pointing to a possible overseas origin.
Still, viewers of these pirated games could be a demanding audience, with many comments complaining about the start-and-stop quality of the video.
"REALLY? just audio??" wrote a Facebook user called Nitrous De Jesus Rodriguez, on a feed titled "NFL Live HD."
CNBC's Michelle Castillo contributed to this report.