Zimbabwean forward Terrence Dzvukumanja gave Wits the lead in the 27th minute, and it got worse for City four minute before the break as defender Ebrahim Seedat was sent off for a second bookable offence.
Wits captain Thulani Hlatshwayo headed in the Clever Boys’ second goal in the 56th minute, as they go to 23 points from 11 games, 11 points behind Chiefs but with two games in hand.
Gavin Hunt’s side, indeed, in fourth position on the log, are just two points behind second-placed Mamelodi Sundowns, with two games in hand and a point behind third-placed SuperSport United, with three games in hand.
City’s disastrous season continues meanwhile, and they have not score a goal in four league games since Jan Olde Riekerink officially took charge at the end of November.
The Cape side are 13th in the table, with 13 points from 15 games, just one point ahead of bottom side Stellenbosch FC.
For more news your way, download The Citizen’s app for iOS and Android.
Download our app and read this and other great stories on the move. Available for Android and iOS.