Gavin Hunt’s men survived plenty of pressure from the hosts at Orlando Stadium before Gladwin Shitolo’s own goal gifted them all three points late on.
The Buccaneers almost went ahead the other side of the break when Pule’s effort beat Keet only to crash back off the post.
Clever Boys took a shock lead on 80 minutes when Shitolo turned Haashim Domingo’s cross into his own net.
There was midweek action elsewhere on Tuesday night as Kaizer Chiefs’ winless start to the season continued with a draw away with Baroka FC.
Amakhosi languish in 13th place on the log, with 2017 champions Wits sitting pretty at the top.