Pakistan made 245 for eight in a rain-interrupted innings which finished with one ball remaining.
South Africa were unable to start their reply because of rain.
The teams will go to the fourth match in Cape Town Sunday with the five-match series tied at one match each.
The tourists were 217 for eight when rain stopped play after 47 overs. Azhar Mahmood and Rana Naved-ul-Hasan added another 28 when play resumed.
The innings ended bizarrely.
With rain falling, the umpires kept the players on the field with Charl Langeveldt bowling what should have been the last delivery of the innings.
It slipped from his hand, Naved swung at it and it sliced over the slips for six as no-ball was signalled because the ball was too high.
With the rain having become heavy and ground staff running on with covers, the umpires took the players off.
No overs were lost during the first break of more than an hour but further rain meant that overs were being reduced before the match was finally called off after two revised start times had been set, only to be foiled by more showers.
The early part of the match was in contrast to Pakistan's run spree in Durban Wednesday when they hammered 351 for four to set up a series-levelling win.
Yousuf and Shoaib Malik (41) put on 91 for the fifth wicket. They took Pakistan from a shaky 71 for four to a position where they could launch an assault. But both men were out in quick succession.
Big-hitting Shahid Afridi, who made an unbeaten 77 off 35 balls in Durban, fell quickly for eight but Abdul Razzaq and Mahmood put on 41 off 38 balls for the eighth wicket before Razzaq was caught behind off Andrew Hall one ball before play was halted for the first time.
Hall, who replaced fast bowler Andre Nel, took four for 35 with his medium pace.
South Africa's bowlers, who took a hammering in Durban, produced a much-improved performance.
Makhaya Ntini gave South Africa an early advantage when he dismissed opening batsmen Kamran Akmal and Imran Nazir in the space of three balls in the sixth over. Both fell to pull shots.
Yousuf had an escape when he was on 24 when television replays suggested he got a faint edge to a ball from Hall which was caught by Boucher. But the South Africans did not appeal.
Yousuf followed up an unbeaten century in Durban with another polished innings, keeping the score moving with deft placements on a pitch which proved to be slightly two-paced and not as good for batting as it looked when Pakistan captain Inzamam-ul-Haq won the toss.
Hall was somewhat lucky to pick up his first wicket when Younis Khan chased a wide ball and was caught behind. But he bowled intelligently, mixing up his pace and getting reverse swing in the second half of the innings.
Hall played because Nel cut a foot when a soft drink bottle fell on it after the second game. Nel is not expected to play in the rest of the five-match series which ends in Johannesburg Wednesday.
Pakistan 245 for 8 in 49.5 overs (Mohammad Yousuf 79, Shoaib Malik 41, Abdul Razzaq 27, Azhar Mahmood 26 n o; Andre Hall 4 for 35, Makhaya Ntini 3 for 53) Vs South Africa (Match abandoned due to heavy down pour)