The New Zealanders were 159 for two in reply to the Rest of South Africa's 395 all out when bad light stopped play but the tourists were hit by an injury to strike bowler Shane Bond.
The Black Caps ripped through the Rest's batting Saturday, taking seven wickets for 40 runs, but Bond did not take the field because of a swollen right knee.
It was announced he would not play again during the match, although he was expected to be fit for the first of three Tests, starting at Centurion on April 15.
After a poor first day, in which the Rest scored 355 for three, the tourists struck early Saturday when Jean-Paul Duminy was caught at slip off fast bowler Chris Martin after adding only two runs to his overnight 125.
Three more wickets fell cheaply before Neil McKenzie, the Rest's captain, was eighth out for 141, having eked out only 16 runs in 24.2 overs Saturday after being unbeaten on 125 overnight.
Left-arm pace bowler James Franklin added three wickets to the one he took on the first day to finish with four for 80.
New Zealand's opening batsmen were dismissed in successive overs early in the touring team's reply. Michael Papps was caught at third slip off Monde Zondeki in the sixth over and Jamie How was trapped leg before by Garnett Kruger seven balls later.
Coming together at 26 for two, Fleming and Peter Fulton added an unbeaten 133 for the third wicket before bad light stopped play half an hour after tea.
The left-handed Fleming was the dominant partner, making his 96 off 96 balls with 15 fours and four sixes, two of them pulled in one over from Kruger, who was earlier named in the South African squad for the Test series.
Fulton was unbeaten on 36 off 84 balls with seven fours.