The match in Santiago's National Stadium, played with 16-man teams and with two halves of 20 minutes each, ended 3-2. The miners had led temporarily with a free-kick goal from Franklin Lobos, a former Chile international.
Pinera, who played centre-forward in a team that brought him together with his advisors, members of the rescue teams and some journalists, scored his side's second goal to launch the comeback.
"The miners were lacking a bit of physical condition, but they had enough technique, and Mr Franklin Lobos proved it with a goal that I had watched him score many years ago against Cobreloa," Pinera said.
When he announced the match days ago, Pinera had joked that the losers would have to go back to the mine."We made a bet, and men keep their word and pay off their bets. The winning team was to go to La Moneda and the losing team was to return to the bottom of the mine. Is that so or is that not so, Mr Franklin Lobos?" Pinera joked in the wake of the win.
"Yes, we're going to have to return to the bottom of the mine," a resigned Lobos admitted, to keep the joke alive.
Earlier, a presidential medal ceremony had provided a chance for an emotional meeting between the freed men and rescue teams. They wept together and shared embraces.
"We always felt the support of everybody," said mine worker Lobos.
"We are completely grateful to all those who fought for us. It was something we could not have imagined," shift boss Luis Urzua said in the ceremony at Chile's presidential palace, La Moneda, in Santiago.
The miners were trapped underground when the shaft they were working in collapsed Aug 5. For 17 days they had no contact with the surface, until they were located and supplied with food, water, oxygen and even communications and television through small exploratory shafts drilled by rescuers.
The men were finally lifted to the surface through a larger shaft Oct 13.
Pinera thanked rescue teams for their efforts and noted that Chile has to draw lessons from the tragedy, with a new approach to labour relations.
One of the miners, Mario Sepulveda, said that their plight under the Atacama Desert should be used as an opportunity for change: "This is the time we have to start reviewing things. This is the time we have to fight for workers to be treated with dignity."
Pinera, accused by some in the Chilean opposition of exploiting the rescue politically, recalled the tension of the spectacular operation.
"We were searching blindly. We did not know where you were, and the truth is we were not sure that you were alive," he told the miners.
The men received medals in the same order that they emerged from the mine.