"I went back to my seat, I ordered a beer - a Heineken beer - and then, little by little, I swallowed that first page of the passport," Abreu said.
With that task accomplished, Abreu was able to remain in the US and eventually seek permanent resident status under the country's wet foot, dry foot policy, which stated that any Cuban intercepted on the waters between the two countries would be returned but those defectors who reached American land would be allowed to stay.
The policy, eventually ended by President Obama as the relationship between the two countries finally warmed, created plenty of accounts like that of Abreu, not least among his fellow ball-players.
Desperate to escape the oppressive regime of Fidel Castro and pursue their American dream, these athletes' journeys are marked by stories of murder and kidnappings, of death threats and human trafficking.
And stories like that of the late Jose Fernandez, who in the middle of the night, while making his way to America on an overcrowded boat, heard a fellow passenger fall overboard and leapt into the dark waters to mount a daring rescue, discovering only then he had saved the life of his mother.
Baseball is better for the presence of those men - just as the US is better because of its immigrants.
Red Sox sleeping on the jobAnd who wouldn't want to play baseball in the US when they have facilities like those being pioneered this season by the Boston Red Sox?
Ahead of the new season, Major League Baseball is so far along the path of analytical awakening that teams these days can rarely exploit an unknown statistical insight to snap up a player underappreciated by others, so franchises are instead looking for competitive advantages in alternative avenues.
Chief among the current areas of research is chemistry in the locker-room. Happy players, teams believe, should equal good players. So how do they turn 25 diverse and egotistical men into one big happy family?
And while that complex equation has yet to reach a satisfying solution - at least not one these secretive franchises is telling us - every parent knows of at least one way to ensure rowdy children behave themselves: getting the little terrors to take a nap.
With that undoubtedly in mind, the Red Sox have this year became the first major league team to install a specialised sleeping room in their ballpark, extending the franchise's relationship with a "performance bedding" company.
What's a sleeping room, you ask? And is performance bedding as made-up as it sounds? Well, the latter entailed the players spending a week testing mattresses, being fitted for personalised pillows and choosing from a selection of blankets and sheets, all of which sounds amazing to someone as fond of sleep as me.
And the former is a lovely new room at Fenway Park where all that performance equipment will be kept, decked out in oak floors, exposed brick and plenty of other nonsense that apparently helps humans enjoy some quality shut-eye.
Now, getting adequate sleep will obviously have physical benefits, but I like to think that regular naps will also help ensure the Red Sox are a little less cranky the next time they're swept by the Yankees.