The broadcasters ended their live showing of the match minutes before O'Sullivan, who was returning to the game after almost a year out, secured a 10-4 victory on Saturday evening.
Instead, they pulled away from the World Snooker Championship and continued their scheduled 8pm showing of an episode of 1970s comedy Some Mothers Di 'Ave 'Em, prompting Hearn to take action.
Hearn wrote on Twitter: "Sorry to all snooker fans for the poor BBC coverage last night. Letter of complaint sent to @BBC today."
In reply, the Daily Mail quotes the BBC as saying: "We're obviously disappointed that we weren't able to show the conclusion to the World Championship Snooker on BBC2."
The coverage of the game was not shown on the red button after it was removed from the main channel, despite the BBC using that option in the past.