With Chiefs already safely into the final, United had to come from a goal down to claim the lead with second half strikes from Kermit Erasmus and Clifford Mulenga. This after Tintswalo Tshabalala had handed Stars the lead midway through the first half.
Then, with the game reaching its conclusion, Stars fought back to level the game at 2-2 with a 90th minute Thabani Mthembu penalty.
In extra-time, veteran Sibusiso Zuma's spot-kick secured Matsatsantsa's passage to the May 25 final.
Stars showed their intent early on, testing SuperSport goalkeeper Ronwen Williams from long-range, before Thuso Phala and Henrico Botes saw their efforts go wayward.
At the other end, chances fell to Sameehg Doutie and Zuma, but neither was able to make their presence felt in front of goal.
Then, in the 25th minute, Dikwena took full advantage of a lapse in the SuperSport defence, allowing Phala to be put through on goal.
Williams rushed out to meet the speedy winger on the edge of the area, squirting the ball to the right and into the path of an oncoming Tshabalala, who made no mistake as he slotted home the opener.
Heading into the break a goal down, SuperSport responded just five minutes into the second period through Erasmus's superb volleyed effort.
A neat ball over the top of the Stars' defence was met with a first-time thunderbolt from Erasmus, who beat goalkeeper Dambe Kabelo to the far post for the equaliser.
With their tails up and looking dangerous, Doutie came agonisingly close to doubling the visitors' tally, but rattled the crossbar with his stinging effort.
The contest settled down until 12 minutes from time, when United showed their pedigree as Mulenga bundled over the line to steal the lead.
A scramble inside Stars' crowded penalty area saw bodies flung towards the ball, before Kabelo spilled United's initial attempt, leaving Mulenga unchallenged just metres out and was gifted Matsatsantsa's second.
Seconds from the final whistle, Stars received a gift of their own, when Phala was brought down inside the penalty area, leaving referee Jerome Damon no choice but to point to the penalty spot.
Williams made a superb stop to deny Mthembu from levelling but, to United's dismay, Damon ordered the spot-kick to be retaken, due to an infringement by United.
Mthembu stepped up and made no mistake from his second attempt, sending the teams into extra-time locked at 2-2.
Stars' hopes were dashed in extra-time, after Damon again pointed to the penalty spot, allowed Zuma to send Mthembu the other way, reclaiming the lead and seeing out a nervy finish in the five-goal thriller.