SA skipper Smith and de Villiers also crafted half-centuries.
Earlier Elton Chigumbura and Gary Brent helped Zimbabwe recover from a disastrous start to a decent total 206 in the stipulated 50 overs.
Tight bowling from the SA seamers reduced the hosts to 72 for 7 before Chigumbura (59) and Brent (59*) chipped in to rescue their side with a fine 115-run partnership for the eighth wicket stand.
Former skipper Taibu, who is back in Zimbabwe squad after a two-year long exile, scored a brisk 22 including 4 hits to fence before cutting Morkel's away going delivery only to give a regulation catch to de Villiers stationed at point region.
For SA right-arm medium pacer Vernon Philander claimed 2 for 15 off eight overs and seasoned campaigner Shaun Pollock also produced a miserly spell conceding just 25 runs accounting Sibanda in 8 overs.
Loots Bosman fell third ball in reply but Bodi and skipper Graeme Smith (50) added 73 to steady the Proteas.
Bodi (51) continued steadily as he put on 74 with AB de Villiers (63) and they eased home with 19 balls to spare.
Skipper Utsyea claimed 2 for 32 in his 10 overs while Chigumbura and Mpofu took a wicket apiece.