His off-colour and at times rambling performance spawned an immediate debate on the Twittersphere between Republicans, who broadly loved it, and Democrats who said the 82-year-old multiple Oscar winner had clearly lost his marbles.
A raucous roar went up from the thousands of delegates as Eastwood, looking frailer than the gunslinging cowboys he portrayed in his spaghetti Western heyday, stood onstage and grilled the imaginary Mr Obama for failing to revive a flagging economy.
“I think possibly now it may be time for somebody else to come along and solve the problem,” Eastwood said during an address in which he taunted Vice President Joe Biden and talked about the detention centre at Guantanamo.
The Oscar-winning director of Million-Dollar Baby and star of Spaghetti Westerns like The Good, the Bad and the Ugly looked down several times at the empty chair, as if he was listening to Mr Obama criticise Republican presidential nominee Mr Romney, whom Eastwood has endorsed.
“He can’t do that to himself. You’re absolutely crazy!” the actor/director responded.
“You’re getting as bad as Biden. Biden is the intellect in the Democratic Party. It’s just kind of a grin with a body behind it.”
“And I thought, well closing Gitmo, why close that, we spent so much money on it. But, I thought maybe as an excuse – what do you mean shut up?” he said to laughter from the crowd.
Eastwood spoke about how he had been moved by Mr Obama’s message of hope and change in 2008 but then grew disillusioned by failed policies and Mr Obama’s inability to reduce the unemployment rate below eight per cent.
“I think it may be time for, what do you think, maybe a businessman,” said Eastwood, referring to Mr Romney.
“When somebody does not do the job, you’ve gotta let them go,” he said of Mr Obama, as he then drew a finger sharply across his throat.
The awkwardness of Eastwood’s rant seemed magnified given that he was taking up a prime spot on the climactic day of the convention that nominated Mr Romney as the challenger against Obama in the November 6 election. But the Romney campaign insisted there was no harm, no foul.
“Judging an American icon like Clint Eastwood through a typical political lens doesn’t work,” a spokesman for the campaign said in a statement.
“His ad-libbing was a break from all the political speeches and the crowd enjoyed it.”
Eastwood’s 12-minute appearance exploded Twitter and other social media, where the fad suddenly slapped with the hashtag #Eastwooding – in which people post photos of empty chairs – spread like wildfire.
Mr Obama himself got into the act, tweeting “This seat’s taken” to his 19 million followers and attaching a link to a fundraising web pag.
Clint Eastwood addressing an empty chair as if it were US President Obama, during the final session of the Republican National Convention in Tampa, Florida.