The striker, a £400,000 January signing from Charlton, scored twice in the first half before completing a perfect display with a third midway through the second period.
Harry Arter added two goals of his own in the second half as the Cherries completed their first league double of the season.
Rovers goalkeeper Sam Johnstone kept Doncaster in the game with a string of impressive saves as the hosts dominated a one-sided first half.
He denied Kermorgant in the fourth minute when he comfortably held on to the Frenchman’s downward header.
Ryan Fraser was the next to be kept at bay by the Manchester United loanee after good interplay down the left flank with Andrew Surman in the 14th minute.
In the 20th minute Bournemouth had a trio of good chances to stamp their dominance. First Fraser’s attempt was blocked by Bongani Khumalo and, from the resulting corner, a well-worked routine forced Johnstone to deflect Surman’s curler before Kermorgant slashed wide.
However, Kermorgant produced the opener six minutes later, volleying in Ian Harte’s well-placed cross for his first Bournemouth goal.
The former Leicester man hit the ball under the body of Johnstone, who will have felt he could have done better with the shot.
Fraser was denied again in the 42nd minute after being set clean through by Kermorgant, but Johnstone dived well to his right.
But Kermorgant struck again a minute before half-time, powerfully nodding in Simon Francis’ hanging ball at the back post.
Doncaster manager Paul Dickov made a double half-time change as he sent on Theo Robinson and David Cotterill in a bid to stem the home side’s dominance.
It only took five second-half minutes for Bournemouth to add to their tally, as Arter drilled a left-footed strike from the edge of the area for his second goal of the season.
Kermorgant then completed his hat-trick in the 73rd minute as he once again met a perfect Francis cross to powerfully nod past the goalkeeper.
Bournemouth goalkeeper Lee Camp was called into action for the first time in the 75th minute when Robinson weakly volleyed straight at him.
He was tested again two minutes later as a miscommunication with captain Tommy Elphick led to Paul Keegan headed towards goal, but Camp clung on to the feeble effort.
Arter added his second in the 82nd minute, this time with his right foot, as Johnstone could only punch Harte’s corner to the Irishman on the edge of the penalty box.
To add to Doncaster’s misery, referee Darren Sheldrake booked Gabriel Tamas, Keegan and Khumalo.