Leicester were in command after Jamie Vardy's scrappy first-half goal. But with the relegation trapdoor creaking underneath their feet, Bournemouth turned the match around in stunning fashion with Dominic Solanke scoring twice.
Junior Stanislas equalised from the penalty spot in the 66th minute after a mistake by Leicester keeper Kasper Schmeichel, who was at fault again one minute later when he allowed Solanke's shot to trickle over the line.
To make matters worse for the Foxes, defender Caglar Soyuncu was shown a straight red card after tangling with Callum Wilson immediately after Bournemouth's goal.
Leicester then collapsed in alarming fashion.
Stanislas's shot in the 83rd minute went in off Leicester defender Jonny Evans before Solanke seized on more dreadful defending to add his second.
With Aston Villa winning earlier in the day, Bournemouth began the match second from bottom, six points behind fourth-from-bottom Watford. The victory - their first since Feb. 1 - means that with three games remaining they still have hope of securing a sixth successive season of top-flight football.
They moved back above Villa to 18th place on 31 points, three behind both Watford and West Ham United, who face each other in the next round of fixtures.
"We needed to change things at halftime and had the mentality that we had to go for it," Bournemouth boss Eddie Howe said. "Thankfully we were able to swing things round."
"I didn't see that coming but we are not good enough to get too comfortable," Leicester manager Brendan Rodgers said.
"We were in control of the game. But we let them into the game with a penalty and I was very disappointed with how we played from there."