South Africa, who were put into bat, were 128-2 after 16.1 overs when the lights went out on one of the four towers with officials reportedly seeking to get a back-up generator working.
Henry Davids hit 55 off 38 balls and captain Faf du Plessis was unbeaten on 48 off 35 deliveries at the stoppage.
The match eventually restarted but was reduced to a 19-over per side game.
"Our sincerest apologies for the delay," tweeted Cricket South Africa.
The home side won the first match in Durban on Friday by eight wickets.