Keene, a former Portsmouth, Djurgadens and Halmstad striker, enjoyed a memorable bow as he provided an assist for Phakamani Mahlambi's opener before scoring just after the break at Nelson Mandela Bay Stadium.
Andile Mbenyane reduced the deficit in the 53rd minute for the Chilli Boys, but Ben Motshwari sealed the result in stunning fashion with 14 minutes to go in Port Elizabeth.
In the beginning of the contest, it was Wits who started better and their efforts were rewarded in the eight minute when a cross from the left found Keene, who laid the ball to Mahlambi and he easily beat Daniel Akpeyi at his near post.
As Dan Malesela’s men tried to respond with a goal, Aristide Bance's long-range effort went wide in the 18th minute, failing to trouble goalkeeper Moeneeb Josephs.
In the 26th minute, Bance proved to be a handful for the Clever Boys’ defence and he unleashed another shot at goal, but Josephs was equal to the task as he parried the ball to safety.
After 30 minutes into the encounter, the Chilli Boys were too strong for Wits and William Twala saw his attempt sailing wide of the posts.
However, eight minutes later Mahlambi tried a long-range shot but it went straight to Akpeyi.
It was 1-0 at the interval and the second stanza saw the visitors grabbing their second goal when Keene finished with his right foot in the 47th minute, beating Akpeyi for the second time.
As the match became a tightly-contested affair, a cross from the left met Bance in the 50th minute but his header went wide.
Three minutes later, a free-kick down the right flank was flicked on by Mbenyane, who beat Josephs at the near post making it 2-1.
Towards the 70th minute, the Chilli Boys were all over the Students and Twala produced some skill on the left before delivering a great cross for Buyani Sali, however, the latter failed to connect with the delivery and his attempt went wide.
Against the run of play, United failed to deal with a cross from the right and Ugonna Uzochukwu tried to clear the ball but it fell in Mosthwari’s path and he made it three with a powerful drive to beat the Nigerian keeper.
In the last six minutes, skipper James Okwuosa nearly bagged a second one for the hosts when he met a corner but the free header went inches wide.
With one minute to go, Okwuosa attempted to catch Josephs off his line, but the ex-Bafana Bafana keeper was alert and fisted the ball over.