The Lions, just one place above the relegation zone in rugby league’s second tier, and forced into fielding three debutants by injuries, trailed three times and looked like their brave effort would be in vain when Izaac Farrell converted Oliver Roberts’s 66th-minute try to give the Giants a 24-20 advantage.
But Swinton, who had previously led 10-6 and 22-18, refused to give up on their dream and Waterworth’s winner was little more than they deserved in a nip-and-tuck contest which could have gone either way.
The Lions were grateful for tries from Shaun Robinson, Rhodri Lloyd, Michael Butt, Connor Dwyer and Waterworth, while the Giants replies came from Aaron Murphy, Sam Wood, Darnell McIntosh and Roberts.
It was Huddersfield, now without a win in nine games, who made the early breakthrough when Kruise Leeming forced a break down the left and Murphy finished in the corner.
Farrell, son of 1999 Leeds Challenge Cup winner Anthony Farrell, converted from the touchline.
Swinton, who last won the cup in 1928, hit back swiftly when Robinson dived over in the corner, but Chris Atkin could only strike the upright with his attempt to add the extra two points.
Dwyer was then held up, as the lower-league side continued to press, but shortly afterwards the Lions did go ahead as Welsh international Lloyd crossed in the other corner.
Atkin this time adjusted his angles correctly with the boot to leave the visitors leading 10-6.
Their advantage lasted only six minutes as Wood charged over and Farrell added the second of his four goals.
Then, on the half hour mark, Farrell put in a neat grubber for alert full-back McIntosh to pounce on but Swinton refused to fold and hit back before half-time, again exposing their hosts’ right-hand defence through a Butt try.
Atkin again judged the touchline kick to perfection to leave just two points between the sides at half-time.
Tempers flared early in the second half and Giants’ Sebastine Ikahihifo and Lions’ Anthony Bate were sin-binned for fighting.
Less than a minute after it became 12-a-side, Dwyer scored to put the Championship side ahead once more and Atkin added his third goal to make it 22-18 to the visitors.
A buoyant Swinton now tackled as if their lives depended upon it, yet were further stretched when losing Adam Jones to injury before the hour mark.
Leeming went close, being held up over the line, then Farrell lost control as he charged for the line, before Roberts ran onto a Lee Gaskell pass to level matters and Farrell maintained his 100% kicking record to edge the Super League side back in front.
But the game was not over and Waterworth pounced with just five minutes remaining, Chris Hankinson adding the final goal.