United took a 15th-minute lead when Chris Wood thumped home Charlie Taylor’s inch perfect cross but Hull scored two goals in first-half injury time through Abel Hernandez and Tom Huddlestone.
Leeds then squandered a golden opportunity to level eight minutes after the break when Wood’s low penalty was brilliantly saved by Allan McGregor.
But United bagged themselves a share of the spoils with two minutes left when great work from Jordan Botaka worked space for Dallas to fire into the bottom right corner.
Whites head coach Steve Evans made two changes to the line up that started against Wolves with Liam Bridcutt and Stuart Dallas replacing Luke Murphy and Lewie Coyle.
Hull boss Steve Bruce brought in Jake Livermore and Chuba Akpom for David Meyler and Adma Diomande who both started in Tuesday’s win at Reading.
And it was the Tigers who did all the early pressing with Akpom twice threatening, first when his low shot was deflected wide by Liam Cooper and then shooting straight at Marco Silvestri from the edge of the area.
Huddlestone then blazed just wide from long range and United’s first foray did not arrive until the 13th minute when Sol Bamba received the ball unmarked at the back post from a Taylor free-kick but was unable to get an attempt on goal.
But just two minutes later United took the lead when a sublime left flank delivery from Taylor found an unmarked Wood who slotted home from six yards.
Hull nearly leveled just three minutes later when the dangerous Akpom fired a rising shot at Marco Silvestri who brilliantly tipped the ball over the bar.
A wild clearance from Taylor then ballooned narrowly wide of the Whites net to avoid what would have been a spectacular own goal.
At the other end, Lewis Cook then raced in on goal from the right flank but his touch let him down and allowed Allan McGregor to smother with Cook wanting a penalty.
Bamba was then booked for a late lunge on Hernandez but Hull’s chances were limited though Harry Maguire’s effort from outside the area pinged just past the left hand post.
An attempt from Moses Odubajo then hit Taylor’s foot and looped just over the bar.
The Tigers were turning the screw and with Leeds sitting too deep it was no surprise when the hosts leveled in the first minute of injury time when a low right wing delivery from the excellent Robert Snodgrass was smashed home by Hernandez.
And just two minutes later the Tigers sealed a dramatic turnaround when a 20-yard low shot from Huddlestone was rifled into the bottom left corner.
The goal was scored ten seconds after the third minute of the three minutes added injury time.
Evans hauled off Erwin for Jordan Botaka during the interval and United were handed a lifeline in the 53rd minute when Odubajo scythed down Taylor just inside the area for a stone-wall penalty.
Wood stepped up looking to bag his second of the game but Allan McGregor produced a superb save at full stretch to his left hand side.
Wood was left to hold his head in his hands and City almost rubbed salt into the wound by bagging a third with Silvestri doing well to stop a thumping header from Hernandez.
Snodgrass then twice went close to bagging the goal his performance deserved as Hull again began to dominate.
With 16 minutes remaining, United then saw Gaetano Berardi stretchered off after a tackle from Jake Livermore who was booked.
After Akpom had shot wide from range, Wood was again denied by McGregor with the ‘keeper standing firm to keep out the striker’s header.
But United were to serve up one final twist in the 88th minute when Botaka worked the ball to Dallas who squeezed the ball home inside McGregor’s right sided post.
Hull City: McGregor, Odubajo, Maguire, Davies, Robertson, Snodgrass, Livermore, Huddlestone, Maloney (Clucas 81), Hernandez (Diame 68), Akpom (Diomande). Subs: Jakupovic, Bruce, Hayden, Elmohamady.
Leeds United: Silvestri, Berardi (Coyle 74), Bamba, Cooper, Taylor, Bridcutt, Diagouraga (Murphy 56), Cook, Dallas, Erwin (Botaka 45), Wood. Subs not used: Peacock-Farrell, Wootton, Phillips, Antenucci.
Referee: Iain Williamson (Berkshire).