Both sides scored three tries apiece and with the scores tied at 22-22 with just three minutes remaining on the clock, it was up to Swiel to decide the outcome of this closely fought coastal derby.
He stepped up to steer his second penalty goal of the game through the poles to earn the Capetonians a morale-boosting win and their second one on the bounce following last weeks' narrow win over the Emirates Lions in Johannesburg, where Swiel also kicked the winning points.
The DHL Stormers led 12-10 at the break following a brace of tries through Edwill van der Merwe (left wing, pictured above), with Abner van Reenen (flyhalf) slotting one conversion.
Cell C Sharks prop Ox Nche scored the first try of the match, which Curwin Bosch (flyhalf) converted in addition to a long range penalty goal.
The DHL Stormers' experienced front row failed to fire for much of the first half, but they managed to shift into a higher gear towards the end of the opening spell to give their side a solid platform and to wrestle the initiative and lead away from the home team.
While it was the Cell C Sharks who dominated possession and territory for much of the first half, they failed to translate those advantages into clear cut scoring opportunities. They made far too many errors when on attack while they also could not handle the visitors properly at the breakdown.
The Durbanites drew first blood when Bosch slotted a long range penalty goal to go 3-0 up. With the home team enjoying possession and territory, it was just reward when Nche planted the ball behind the goal line after several strong surges by the home pack. Bosch easily converted to hand his side a deserved 10-0 lead.
The DHL Stormers were their own worst enemy in the opening 20 minutes by conceding seven penalties, which allowed the home side to enjoy most of the initiative on attack.
Van der Merwe grabbed the visitors' first try through a superb solo effort when he collected the ball in his own half to switch on the turbo and beating several defenders on his way to the try line. Van Reenen converted to close the gap to 10-7.
The diminutive speedster was at it again five minutes before the break when he was on hand to gather a pass from Springbok fullback Damian Willemse to score out wide. This unconverted try gave the men from the Cape the lead for the time while the score also signalled the swing in dominance in favour of the visitors.
The DHL Stormers started the second half in the best possible way when towering Springbok loose forward Pieter-Steph du Toit ran in from 40 meters out for his side's third try, which Van Reenen converted (19-10).
However, the home response was swift through a cleverly executed try scored by left wing Yaw Penxe, with Jaden Hendrikse (No 9) and Siya Kolisi (flank) prominent in the build-up.
The KwaZulu-Natalians then were fortunate to score again via a converted Aphelele Fassi (fullback) try. Van Reenen failed to complete a pass, with Fassi reacting the quickest to kick the ball ahead, gather and score under the posts. That converted try handed the lead back the home team with the score at 22-19 in their favour.
Second half replacement Swiel (on for Van Reenen) then proceeded to succeed with his first penalty goal attempt to draw the teams level at 22-22 before kicking over the winning field goal towards the end.
Cell C Sharks 22 (10) - Tries: Ox Nche, Yaw Penxe, Aphelele Fassi. Conversions: Curwin Bosch (2). Penalty goal: Bosch.
DHL Stormers 25 (12) - Tries: Edwill van der Merwe (2), Pieter-Steph du Toit. Conversions: Abner van Reenen (2). Penalty goals: Tim Swiel (2).