But just how special, he cannot have known. The story since September of Mr Ozersky, a 26-year-old research scientist, will be familiar to lottery winners. What he got in Busch Stadium was a windfall, literally. He has yet to collect his winnings - that should happen next Tuesday in New York.
McGwire had, of course, already broken the 61 single-season home run record set by Roger Maris in 1961.
As he raised his bat that day, he had the stadium in his thrall. Would the ball fly over the fence just one more time? And if it did, who, among the tens of thousands watching, would catch it?
When a home run is scored, identifying where exactly it lands in the terraces - always assuming it doesn't travel clean into the car park - is never difficult. You will instantly spot that small zone of human convulsion, where fans near enough to where the ball falls will simultaneously lunge to retrieve it. Under baseball's rules, it is finders keepers.
Now there are baseballs and baseballs. Never mind that they all look exactly the same and can be bought for a few dollars in any sporting goods shop.
To fans, balls that have been whacked for a home run are special trophies. Those who snag one usually have a choice - to keep it or to return it to the player who hit it in return for autographed club souvenirs. But at this moment, there was the chance to capture the veritable Holy Grail of the sport - the ball that would set the new home run all-time record.
It was an instant Mr Ozersky has since played over in his mind many times. On that first pitch, McGwire struck the ball with a thwack. It soared, it peaked against the St Louis sky and arched down directly into the box occupied by Mr Ozersky and his colleagues. Within a split second, he was on the ground beneath the benches temporarily installed for the game, desperately reaching for the prize. And suddenly, he had it, right there in his hands. The life of Philip Ozersky was altered for ever.
As if out of nowhere, a team of security men was in the box and escorting the delirious Mr Ozersky to a private room beneath the box. They first authenticated the ball and then offered him the usual choice of returning it to McGwire. Mr Ozersky, however, hesitated. Instead, he took the ball home and that night slept with it hidden in a drawer in his bedroom. He took it to work the next day to show it to his friends then decided to lock it in a security deposit box at his bank.
A cousin in Florida who is a lawyer stepped in to help. Giving the ball away was quickly ruled out because of crippling gift taxes. Selling the ball in tiny bits, thread by thread, was also eliminated. Finally, contact was made with an agent in St Louis who persuaded Mr Ozersky that the best route was to put the ball up for auction. He also arranged to have the ball delivered to a firm in California that tagged it with a smear of synthesised DNA. The DNA tag will ensure that the identity of the ball is never called into question.
And so next Tuesday, in Madison Square Garden in New York, the ball that McGwire put away on his 70th and final home run of the extraordinary 1998 season will go under the gavel. Selling it will be Guernsey's, the New York auction house.
A pre-auction of the ball started yesterday on the Internet. The top three bidders from the cyber auction will join the live sale.
It is only a ball, but most experts expect it to sell for $1m or more. Mr Ozersky will certainly be hoping so. In the past few weeks he has fended off countless private offers for the ball - one, involving three partners, for $1m.