The 26-year-old Scot's victory at Meadowbank also ensured he stretched his unbeaten record to nine fights.
Joubert, 35, came into the bout having lost only four of his 35 fights and he managed to inflict Taylor's first cut as a professional.
That, however, did nothing to stop the man from Prestonpans sealing the win.
Taylor, who with every triumph is edging closer to a British title fight, had admitted before the bout that he knew very little about his opponent.
That contributed to a cagey first round from both but the Scot undoubtedly held the advantage over the more experienced South African.
And the Glasgow 2014 Commonwealth Games gold medallist upped his work-rate in the second round, catching Joubert with a sharp left hook early on that had him rocking on his heels.
Taylor picked up a cut in the early rounds but it was unclear whether that was the result of a shot or a clash of heads.
The Scot maintained his offensive intensity in round three with a flurry of punches to the body that sapped the energy from his rival. Joubert could not cope with Taylor's hand-speed and time and again he was forced back into the corner of the ring.
In the fifth round Taylor looked to press home his advantage, having clearly worked out his opponent's style and found holes in his defences. Another trademark left hook shook the South African but the round finished before the Scot could inflict any more punishment.
The bell only delayed the inevitable, though, and after one minute and 27 seconds of the sixth round Taylor unleashed a series of punches that left Joubert on the deck. The South African got to his feet but his corner had thrown in the towel before the referee could count to 10.
It was a well deserved win for Taylor, who has previously expressed a desire to meet countryman and WBA super lightweight champion Ricky Burns in a Scottish super-fight.
Josh Taylor successfully defended his Commonwealth super-lightweight title with an impressive sixth-round stoppage of South Africa's Warren Joubert.