Soon after, he received another call that his father had passed away from silicosis, a condition that results from dust build-up in the lungs.
It was a day that understandably changed his life.
Oliver, who had lost his mother when he was 11 years old, would have to tackle the rigors of professional sports without the two biggest influences in his life.
In addition, the 21-year-old Ohio native would have to do so as a replacement parent, as he raised his younger brother and a teenage sister who was pregnant.
Facing such hurdles, Oliver accepted his fate.
"I was instilled with great confidence and a strong sense of responsibility," Oliver told the Pittsburgh Tribune-Review. "I had enough common sense to listen to what my parents said and took heed. Everything my dad said to me as a young kid was true. I was taught as a youth to be a self-motivator and to have a standard of high self-esteem."
Oliver used those values well, overcoming his difficult situation to churn out Hall of Fame-type numbers, retiring after the 1985 season after amassing an impressive 18-year career with seven different organizations.
Oliver finished with more than 2,700 hits, a .303 lifetime batting average, more than 500 doubles and 1,300-plus RBIs. He was a seven-time All Star and finished in the top 10 in MVP voting several times.
In addition, he earned a World Series championship ring with Pittsburgh in 1971.
In 1991, it was expected that Oliver's resume would lead to induction into the Hall of Fame.
But not only did the Baseball Writers' Association of America decide not to induct Oliver, having 19 out of 443 votes on the first ballot knocked him out of any future chances.
Oliver gets another opportunity, though, in 2007, as one of 27 former Major League players on the Hall of Fame Veterans Committee ballot.
And the Oliver supporters might descend on Cooperstown in droves to ensure his induction, considering his accomplishments on and off the field.
"It's hard to imagine why Al Oliver is not in the Hall of Fame," said Bill Neri-Amadeo of the Black Athletes Sports Network. "Statistics tell a story and they tell that during his playing career, only Pete Rose and Rod Carew had more hits. However, there is a whole other side to Al Oliver and that side includes public speaking engagements as well as creating a foundation in his name that is dedicated to helping the youth, elderly and veterans build self-esteem through a variety of activities."
Oliver played half of his career with the Pirates, from 1968 to 1977, before being traded on Dec. 8, 1977. He was part of a four-team deal that included the Atlanta Braves and the New York Mets, traded by the Bucs with Nelson Norman to the Texas Rangers.
August Busch Jr.
Oliver spent four years with the Rangers and became the club's all-time leading hitter with a .319 batting average. He reached the club's top 10 in every batting category before being dealt to the Expos in a March 1982 trade for third baseman Larry Parrish.
Playing first base for Montreal in 1982, Oliver batted a career-high .331 and captured the NL batting title while also leading the National League in hits, total bases, doubles, RBIs, runs created and extra-base hits. He made the Silver Slugger team for three straight years and was the first to do so at three different positions (left field in 1980, designated hitter in '81, and first base in '82). He also became the first player to amass 200 hits and 100 RBIs in both the American and National Leagues.
Oliver was involved in trades with the Giants and the Phillies in 1984 and spent the first half of the 1985 season with the Dodgers before winding up in Toronto, for whom he delivered a pair of game-winning hits in the 1985 League Championship Series.
Oliver retired after the 1985 season and ranks in the Majors' all-time top 50 in games played (2,368), hits (2,743), total bases (4,083), RBIs (1,326), and extra-base hits (825). His hits rank 47th on the MLB all-time list and his 529 doubles rank 28th on the all-time list.
He finished second in the 1969 NL Rookie of the Year voting after batting .285 with 17 home runs, and from 1970-76 he helped the Pirates win five division titles, including the World Series banner in 1971. He batted .300 or more 10 times in his career and, despite a relatively low home run total (219), he put up numbers at his position which were the best in terms of most runs created (1,341) during the period from 1961-1999.
Despite these numbers, Oliver was snubbed in the 1991 Hall of Fame balloting, a year after Joe Morgan was inducted with numbers that included a lower career batting average (.271) and lower numbers in hits (2,517), doubles (449) and RBIs (1,134) in more games (2,650).
But Oliver isn't bitter. In fact, he's pleasantly surprised he's been given another opportunity.
"I would never, ever thought I would have a second chance," Oliver said. "Surprisingly, [the low total in 1991] didn't bother me. Everybody else was mad for me. I was disappointed, but never angry."
The Veterans Committee electorate (currently at 83 members), is comprised of the living Hall of Fame members (60), Ford C. Frick Award recipients (14), J.G. Taylor Spink Award recipients (eight) and former Veterans Committee members whose terms have not yet expired (one).
"The only thing I can say is that, sure, the numbers are there," said Oliver. "If they look very closely at the total package, I like to think, if they are fair, there's a good possibility. My suitcase is open."
Chris Girandola is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.