Ross McCormack scored a consolation midway through the second half, but the Cherries celebrated victory over their rivals for the first time in their history.
Bournemouth dominated from the start as Marc Pugh's low drive forced Jack Butland into a smart save at his near post inside 30 seconds.
From the resulting corner, Ian Harte's clever training ground routine found Simon Francis making a late run outside the penalty area, and his shot hit Kermorgant en route into the back of the net.
It was the Frenchman's fourth goal since joining the Cherries from Charlton in January as he knocked the ball in from close range.
Bournemouth had only conceded once in the past six league games coming into the fixture, and the closest Leeds came to testing Lee Camp was a wayward long-range effort from Rodolph Austin.
Bournemouth's leading goalscorer Grabban did not have to wait long to get his 16th goal of the season as he converted Francis' low cross after a rapid counter-attack in the 18th minute.
Winger Matt Ritchie started the attack deep inside his own half before feeding right-back Francis with a defence-splitting through ball, which Grabban swept past Butland.
Grabban added his second in the 28th minute when he smashed a powerful shot under Butland after a scintillating run by Francis.
The right-back, who has played every minute in the league for the Cherries this season, hurdled three weak tackles before back-heeling into the path of Grabban.
In the 31st minute Kermorgant struck the bottom of the post as the Leeds defence struggled with Grabban's pace again.
Bournemouth continued their rout in the second half as Kermorgant started both halves with a goal, when he met Ritchie's pinpoint cross unmarked at the back post in the 50th minute.
In the 64th minute Harte swept in another well-hit corner, but Butland denied centre-back Steve Cook's header with a fine block.
McCormack's in-swinging free-kick came close to grabbing one back in the 66th minute, but neither Tom Lees nor Matt Smith could find contact at the back post.
The winger, Leeds' only stand-out player, did score a consolation goal three minutes later when he turned Cook before sliding past Camp.
Substitute Tokelo Rantie should have added a fifth for Bournemouth in the 79th minute with his first touch after coming on, but he could only tamely hit straight at Butland after clearing the defence.
Rantie had a similar chance in stoppage time after Butland mis-kicked, but the South African once again failed to beat the goalkeeper.