The Springboks, who only saw some 30 percent of the ball in the game, hung on through an anxious last 10 minutes as the visitors came with metres of a last-gasp try that would have handed them a historic victory.
Both sides scored a try with Ireland going over first after 16 minutes when Luke Marshall crashed through the Springbok defence after a strong build up.
South Africa conjured up a clever try on the stroke of halftime as Jantjies kicked up into the left-hand corner for flying win JP Pietersen to snatch the ball out of the air and cross over.
South Africa were again disjointed as a clever Irish side kept asking questions and the tourists went 10-3 ahead with 20 minutes gone.
Marshall's first test try came as Ireland showed patience with ball in hand and put together several key phases to allow the centre to force a break in the home defence.
But the Boks went into a 13-10 halftime lead just before the break after a piece of improvisation from Jantjies found Pietersen with uncanny precision.
In the second half, just nine points were added to the score. A long-range penalty from wing Ruan Combrinck extended the lead on the hour and then Jantjies popped over another penalty to make it 19-10.
Paddy Jackson, who kicked eight points for Ireland, brought it back to a six-point game with 10 minutes to go, sparking a last furious burst from the Irish.
But tenacious home defending kept them away from the try line to hand South Africa an unconvincing series win.
"We grinded it out a bit but it was good to get the win. It was a tough series. The forwards did all the hard work to play the platform today," said South Africa captain Adriaan Strauss.
Ireland won a test in South Africa for the first time when they won the opening encounter 26-20 at Newlands but last weekend went down 32-26 at Ellis Park in the second test.
"We were just inches away, it speaks volumes of our boys. The fact that we were within six points in two tests is a testimony to our players," said Ireland skipper Rory Best said.