Leeds scored four tries to three in the 80 minutes and had several chances to snatch it before Kruise Leeming landed the winning drop goal eight minutes into extra-time.
The game was finely poised at half-time when Hull led 16-14, thanks to a goal after the hooter, but they seemed to be pulling away after adding eight more points in the first 10 minutes of the second period.
Leeds, though, cut the gap to four going into the final quarter and levelled with seven left.
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Having lost Rob Lui to a head injury early on, Rhinos didn’t have a drop goal expert in their side and three different players missed before Leeming kept his nerve to win an absolute thriller.
Rhinos made the better start, going 8-0 ahead after as many minutes.
They tapped back-to-back penalties close to Hull’s line and following the second, Rhyse Martin twisted out of some weak attempted tackles to stretch over for a try which he also converted.
The same player then added a penalty after a late tackle by Connor on Richie Myer, but Hull immediately made Leeds pay for two errors.
Harry Newman knocked-on inside his own half and at the end of the resulting set, Myler couldn’t take Sneyd’s low kick, knocking the ball to Danny Houghton who was gifted the easiest of tries.
Sneyd added the extras and then levelled ther scores, after 16 minutes, with a penalty goal after interference by Matt Prior in front of Leeds’ posts.
That came after Luke Briscoe mis-kicked when Connor put boot to ball and Myler was trapped in goal to concede a drop out.
On 20 minutes Sneyd’s kick was flicked on by Connor to Carlos Tuimavave and he went over at the corner.
Sneyd landed a touchline goal and Ligi Sao got over Rhinos’ line, but was forced over the dead ball line by Prior, Myler and man of the match Brad Dwyer.
Moments later, Rhinos scored their second try through a strong finish by the impressive Newman, who shrugged off Sneyd and got past Manu Ma’u from Leeming’s pass.
Martin converted to level the scores.
Hull - and referee Robert Hicks - thought they had gone back in front three minutes before the interval when Sneyd’s kick was touched by Connor and Andre Savelio touched down.
Video official Ben Thaler decided the ball went forward off Connor.
However, on Hull’s next attack they got a six-again on the final play and penalty in front of the posts for offside and Sneyd made it 16-14 with the final kick of the half.
The scrum-half extended Hull’s lead with another penalty after 47 minutes when Luke Briscoe dropped Connor’s kick and Leeming, who was offside, picked up.
Moments later, Connor landed a 40-20 and sliced through Leeds’ defence in the resulting set and moments later - after Sneyd converted - Tuimavave thought he had scored, but was offside from Connor’s kick.
Leeds countered from the penalty and Leeming began and ended a move also involving Luke Briscoe and Newman.
Martin landed the goal via a post and Leeds had a try ruled out after 63 minutes when Luke Briscoe got over at the corner, but Thaler spotted he had put a foot in touch before getting the ball down, overruling Hicks again.
With seven minutes left, Jack Broadbent - in his first game since suffering an ankle injury in July - went over from Myler’s pass, but Martin - surprisingly - missed the conversion to leave it all square.
Sneyd missed with a drop goal attempt in normal time and Ash Handley almost got over at the start of the extra period, before Leeming’s drop goal attempt went under the bar.
Myler also missed before Newman charged down Sneyd’s kick and in that set Martin had a shot, but hit the bar.
Sneyd’s kick fell short at the start of the second period of extra-time and, with less than two minutes left, Broadbent dived on a loose ball deep in Hull’s territory and Leeming won it with the first drop goal of his career.
The game began 30 minutes late after the previous game - Catalans against Saints - went into golden-point extra-time.
Leeds and Hull had already warmed up outside the stadium, but had another brief work-out on the pitch and stayed out for kick-off.