The world champions wasted no time clinching their bonus point, scoring four tries inside the opening 12 minutes.
Scrum-half Reinach claimed an early double before wing Mapimpi, with his first, and Damian Willemse, also crossed.
Reinach sealed a deserved hat-trick off the back of a scrum and Willemse calmly converted as the Springboks carved out a 33-0 half-time lead.
South Africa started where they left off in the second half through hooker Deon Fourie, who claimed their sixth try of the game in the 43rd minute.
Romania's discipline began to waver and after 54 minutes they gave away a penalty try
Grant Williams weighed in with two tries before Mapimpi, a handful for the Romanian defence all game, completed his hat-trick with two further tries.
South Africa led 71-0 with 13 minutes remaining and Willie Le Roux got in on the act on 73 minutes with the Springboks' final try of a comprehensive victory to add to their opening 18-3 win over Scotland.