Rickelton's career-best 75 and Hendricks' 16th 50 powered South Africa to 2-178 in the 18th over in reply to Ireland's 8-171 on Friday.
Ireland looked like they would pass 180 but lost three wickets in their last over as medium-pacer Patrick Kruger finished with a career-best 4-27 in his fifth T20.
Rickelton's previous best score in six T20s was 27, and he passed that after consecutive sixes off medium-pacer Fionn Hand.
Rickelton then took Matthew Humphreys over cow corner and smoked Ben White over deep midwicket. He reached his maiden T20 50 off 30 balls.
White went for another couple of sixes in the 11th over and South Africa's run rate passed 10.
Hendricks reached his 50 off 31 balls by hitting Hand for six over deep square leg and was out in the next over, pinned in front by Craig Young for 51 off 33. Rickelton was caught in the following over, the 14th, for 76 off 48.
Rickelton and Hendricks scored 136 together and brought the run rate required down to less than a run a ball.
Matthew Breetzke and captain Aiden Markram had no trouble knocking off the last runs and preserving South Africa's unbeaten record against Ireland in T20s.
Ireland started well when Ross Adair took a six and two boundaries off Lizaad Williams in the first over, and Curtis Campher and Harry Tector carried them through the powerplay.
Campher and Neil Rock then combined for 59 in nearly seven overs until Rock was bowled by leg-spinner Nqabayomzi Peter.
Campher, dropped on 17, was caught at the second chance by Ottneil Baartman on the boundary, but only after he had hit 49 off 36.
Ireland were 5-169 going into the last over but Kruger deflated their charge by bowling a brilliant three-wicket maiden over.
The Irish moved the tour to the United Arab Emirates because it was cheaper to organise there than at home. The teams play one more T20 on Sunday then three one-day internationals.
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