Hendricks, who hit three half-centuries in the Proteas' recent 2-1 series win over England, top-scored with 74 in a total of 211-5 and shared a third-wicket partnership of 112 with Aiden Markram (56).
Lorcan Tucker (78) and George Dockrell (43) kept Ireland in the hunt but when the pair were dismissed off consecutive balls their side's hopes of victory went with them.
A target of 37 from the final two overs never looked like being achieved, with Proteas' 'death-bowling' specialist Wayne Parnell proving his worth for all he was hit for six off the last ball off the innings by tailender Barry McCarthy as Ireland finished on 190-9.
Left-arm paceman Parnell returned figures of 2-36, having removed opener Andy Balbirnie, with stand-in Proteas captain Keshav Maharaj taking 2-29 with his left-arm spin and leg-spinner Tabraiz Shamsi 2-37.