Gladwin Shitolo captained Arrows who gave a run to Sibusiso Sibeko and Siphamandla Sabelo in place of the suspended Knox Mutizwa with Romario Dlamini in at right back for Siyabonga Dube.
Excessive rain around the venue coupled with wet pitch conditions saw the start of the match delayed for 30 minutes.
Arrows were off to a fiery start when Zolani Nkombela combined with Sibeko who played in Seth Parusnath for a strike that flew wide.
From a counterattack, VUT stunned the visitors on seven minutes with Nkombelo taken out the equation allowed the hosts a shot outside the area that led to the opener.
The lead lasted only seven minutes as Arrows drew level after Sibeko evaded one challenge to find Sabelo who saw his effort resulting in an own-goal.
A defensive error from Mzwandile Buthelezi nearly put VUT back ahead, but Mlungwana smothered the danger.
Abafana Besthende refreshed their front line after halftime, with Sibeko making way for Michael Gumede. However, the Absa Premiership outfit struggled to get a foothold as numerous chances from Dlamini and Sabelo in particular went begging.
Lindokuhle Mtshali should've given the visitors the lead towards the final quarter, but he blazed Sabelo's cut back over the top.
Arrows hit the front in the final seven minutes courtesy of a bicycle kick from Gumede after a cross from Nkombelo, but VUT responded within a minute to go as confusion at the back culminated in the leveller that sent the game into extra time.
Abafana Besthende continued to misfire in front of goal and sent the match to a penalty shoot-out which VUT won after successfully converting their kicks as Mtshali missed for Arrows.
VUT: Naane, Mokondo, Chesane, Lekalakala, Tema, Bodiba, Sibisi, Mawelewele, Hlongwane, Nampa, Mgidi.
Subs: Makhalanyane, Mabelane, Masango, Khoza, Raseasala, Ntombela, Nkoe.
Arrows: Mlungwana, Nkombelo, Shitolo, Buthelezi, Dlamini, Ndwandwe, Parusnath, Mtshali, Zuke, Sibeko, Sabelo.
Subs: Mbaeva, Bilankulu, Lunga, Conco, Sibiya, Gumede, Khwela.