The Cherries were 2-0 and 3-1 down but an inspired substition from boss Eddie Howe bringing Ryan Fraser on with 35 minutes to go proved to be the difference down on the south coast.
Howe pleased with second half
Howe admitted after the game that something had to be done to prevent Liverpool's total dominance.
"Although our goalkeeper wasn't overworked with saves (in the first half), their dominance of the game was quite evident.
The 39-year-old went on to say, "We had to dig deep, juggle things around a bit at half-time and came out a much better team."
Sadio Mane and Divick Origi had given the visitors the lead with two goals in two first half minutes, before Callum Wilson was allowed to pull one back from the penalty spot on 56 minutes.
Liverpool then re-gained their two-goal advantage just eight minutes later when Emre Can found the top corner of Artur Boruc's net, seemingly putting the game back out of sight.
But cue the Ryan Fraser show, after winning the penalty, the Scotsman scored his maiden Premier League goal before setting up Steve Cook for the equaliser.
Pandemonium then ensued at Dean Court when loanee Nathan Ake popped up in injury time to snatch all three points for Eddie Howe's men.
Howe was delighted with Fraser's impact, who was named man of the match.
"I believe Ryan's an outstanding talent," he said.
"He's been training very well for a number of weeks - he's deserved the opportunity he got today. The pleasing thing for me is that he's come on and taken it."
Howe wasn't finished praising the youngster, as he added "He looked razor sharp, he had a big impact on the game and I'm delighted for him."
The win takes the Cherries back to the top half of the Premier League table, and means Liverpool failed to close the gap on leaders Chelsea.