Bucs have now played to goalless draws in each of their last four League matches and any slim hope they may have had of catching up with the leading duo of SuperSport United and Mamelodi Sundowns has surely been dashed.
Wits started off very positively, winning a number of early corner as they dominated possession and territory.
However, it took them nearly 23 minutes to finally force a genuine save out of Moeneeb Josephs, with Fabricio Rodrigues’ low free-kick being smothered by the former Wits keeper.
Pirates themselves looked fairly pedestrian up-front, with an acrobatic overhead effort from Bennett Chenene that was easily saved by Darren Keet being their only real highlight in an attacking sense in the first half hour.
The Clever Boys were inches away from taking the lead in the 34th minute as Rodrigues unleashed a stab at goal from the edge of the penalty area that rattled the crossbar and bounced away to safety.
Three minutes later Sifiso Vilakazi came close with a glancing header from Thando Mngomeni’s finely measured free-kick; the ball flashed just wide of Josephs’ left hand post.
The Buccaneers should have taken the lead just before half-time with their only clear sight of goal in the first 45 minutes, but Dikgang Mabalane could only find the side-netting.
Pirates were perhaps unlucky to have a strong penalty shout ignored by referee Buyile Gqubule seven minutes into the second half, with Chenene tumbling inside the box under a challenge from Rodrigues.
Pirates tried to turn things in their favour with a couple of attacking substitutions in the final ten minutes, but neither Siphelele Mthembu nor Dennis Masina were able to provide the spark in the final third.