Robinson was sent off in October 2022 for throwing the ball at Swansea's Ben Cabango and his seventh-minute dismissal paved the way for a 2-0 Cardiff defeat.
But Robinson made amends for that moment of madness by sweeping home fellow substitute Ollie Tanner's cross 11 minutes from time and cancelling out Liam Cullen's early strike for Swansea.
It sparked an extraordinary ending as Tanner was injured in the resulting celebration, seemingly after colliding with an advertising hoarding, and Cardiff manager Erol Bulut was sent off for tangling with Swansea substitute Kyle Naughton.
Swansea looked as if they would extend their run of five wins in the last six meetings with their bitter rivals when Cullen prodded home after 10 minutes.
Cardiff had not savoured derby success in front of a Swansea crowd since February 2011.
Their victory in March 2021 came when the Covid pandemic ensured there were no fans present.
Wales striker Cullen rewarded the hosts' early superiority in a fixture not played this early in a campaign since 1957.
Cardiff were on the back foot at the start of the second half as Ronald twice blazed over and the Brazilian failed to pick out the unmarked Cullen.
But the Bluebirds turned to their bench with Rubin Colwill and Tanner sent on to provide attacking impetus.
The double substitution worked to perfection as Colwill and Tanner combined and Robinson ended a 14-game scoreless streak to secure Cardiff's first point of the season.
