The visitors made a good start in West Yorkshire and could have led in the second minute when Enzo le Fee's cutback to the edge of the area was met by Jobe Bellingham but his low shot was too close to Illan Meslier, with the Frenchman then getting up quickly to thwart Patrick Roberts.
Leeds then got on top in terms of possession but struggled to break the well-drilled Black Cats down and were then caught with a sucker punch.
Ballard, who had also set Le Fee going for their early chance, was given too much time to clip a ball into the path of the rampaging Isidor and he showed Premier League quality with strength, skill and composure to score a 12th of the season.
Thereafter the Whites threatened through widemen Dan James and Manor Solomon but a James header hacked away from in front of the line by Luke O'Nien just before the break was as close as they came to levelling.
Barring a very early foray, the Wearsiders were pinned back for much of the second half but Anthony Patterson was only called upon for one fairly routine stop from Joel Piroe before Struijk headed in.
That lifted the energy among the home fans but Sunderland looked like they had done enough to at least claim the point they deserved.
However, with seconds remaining Rothwell collected Largie Ramazani's mishit shot out wide on the right and hammered a vicious cross-shot that beat Patterson's attempted punch and was headed in once more by Dutchman Struijk to spark chaos.
Skipper Ampadu gathered his team into a huddle in the centre circle after the final whistle blew on a night where Leeds showed a title-winning mentality.