The Cherries looked to be heading for all three points when they led by two goals early in the second period, but Sam Greenwood, Liam Cooper and then Crysencio Summerville completed the turnaround for Jesse Marsch's side in the final 30 minutes of action.
The result has seen Leeds rise into 12th position in the table, while Bournemouth sit 15th, just two points outside of the relegation zone, with the visitors suffering their seventh league defeat of the campaign.
Leeds were awarded a penalty with just 50 seconds on the clock, with Marcos Senesi bringing Summerville to the ground, and Rodrigo stepped up to send the home side into a third-minute lead.
Bournemouth were level in the seventh minute, though, with Marcus Tavernier's half-volley finding a route into the back of the net despite the best efforts of Illan Meslier.
The Cherries then came close to taking the lead in the 13th minute when Jefferson Lerma climbed high inside the box to meet a corner, but Pascal Struijk was on hand to clear off the line.
Bournemouth did score a second in the 19th minute, though, with Philip Billing expertly picking out the bottom corner after collecting a pass from Tavernier.
The visitors were full of it, and had two more chances before the 30-minute mark, but Meslier did well to deny Lerma before the Leeds goalkeeper kept out an effort from Kieffer Moore.
Leeds were pushing for a leveller late in the first period, but Brenden Aaronson saw his powerful effort blocked by Lewis Cook after a period of pressure, with the half-time whistle blown shortly after.
Bournemouth scored their third of the match in the 48th minute, with Dominic Solanke brilliantly flicking the ball into the far corner after meeting a cross from Tavernier.
Leeds answered back in the 61st minute, with Greenwood curling a fantastic effort into the back of the net from the edge of the area.
The Whites then levelled the scores in the 68th minute through Cooper, who headed a corner from Greenwood past Mark Travers into the bottom corner.
Jack Stacey fired just wide of the home side's post in the 73rd minute before Jack Harrison had a goal-bound shot blocked down the other end, with both teams pushing for a fourth.
Summerville scored a fourth for Leeds in the 84th minute, though, with the forward converting after incredible work from Wilfried Gnoto, who had carried the ball best part of 50 yards before finding his teammate, and the goal sparked jubilant scenes inside the stadium, with the hosts claiming a huge win.