Well, contrary to what neuroscience was leading me to expect, nearly all of my details check out. The main one that did not was my age – I figured I was 6, but actually I was just a few weeks shy of turning 8, so this hardly counts as one of my earliest memories.
I started off by googling “Steelers 14 Eagles 0”. One of the top hits was for a page on the site footballdb.com, which listed all the times the teams had ever met, which hasn’t been all that many. The only possibility was November 1974, when the Steelers won 27-0. While perhaps I was only remembering the halftime score, the time of year just didn’t seem right. I went to the historical data on weatherunderground.com and, sure enough, Philadelphia was 50 degrees and calm that day.
But I wasn’t looking at preseason games. Not nearly as many people search for these, because I had to go all the way to page 2 of search results before finding anything useful. Once again, footballdb.com was the ticket: Steelers 14, Eagles 7, August 9, 1976; attendance only 16,000, versus over 40,000 for every other preseason game, which seemed consistent with adverse weather.
And so again to weatherunderground.com, where I found that Philadelphia received 1.55 inches of rain, maximum sustained winds of 23 mph and gusts to 39 mph. OK, so not quite a hurricane, but maybe the memory had been exaggerated over time, which is also typical of how our memories tend to work.
Next I searched for a newspaper from the day after. The online archives of the Philadelphia Inquirer and Daily News don’t go back that far, but I clicked on a sponsored link for newspaperarchive.com, which led me to one of the suburban papers. It really was a hurricane!
(to be continued) 
Nice synapses, Frank! Here’s someone else’s childhood Eagles recollection, relayed by a friend (i think?) and now I’m trying to summon it, so I’m SURE it’s wrong. There’s a kid, a drunken deadbeat dad, and a birthday weekend in the greater Philadelphia area. Dad says, kid, I’m taking you to the Eagles game for your birthday. Dad is unreliable so kid doesn’t want to get his hopes up. Dad’s on a bender that weekend. But sure enough, Sunday, he shows up and takes the kid to the stadium. They approach the gate but stop short. Dad punches kid in the arm really hard. Brings crying kid up to the gate. “Some guy just ran off with our tickets,” dad says to ticket-taker. He lets them through.