Gianfranco Zola's men had not won in seven before the clash, but appeared set to change when they took a 2-0 lead into the break thanks to goals from Deeney and Christian Battocchio.
Leeds - on a run of five straight home wins - roared back at them, though, and with 12 minutes left were ahead thanks to a thrilling comeback started by Danny Pugh, extended by Matt Smith and finished by the in-form Ross McCormack.
But there was still time for more drama as Deeney cashed in after Paddy Kenny failed to deal with George Thorne's long-range grass-cutter.
A draw was a fair result at the end of a barnstorming clash which followed on from the two meetings between the sides last season.
Then, Watford won 6-1 at Elland Road and then missed out on automatic promotion as United earned a last-day win at Vicarage Road in controversial circumstances, so another classic was perhaps always on the cards.
Smith was first up with a header which Jonathan Bond held, before Deeney was also unable to find the net with his head at the other end.
Home skipper Rudy Austin then broke through and drove straight at Bond, with Luke Murphy wildly failing to find the open goal on the rebound, before Kenny had to make his first save as Ikechi Anya fizzed in a shot.
Watford looked the more composed of the two sides, though, and showed it on 12 minutes as they took the lead. Lewis McGugan bundled into the box and, after he was stopped, Deeney was on hand to fire in a fine 10-yard shot.
Leeds' response consisted of a penalty shout as Smith went to ground and a shot wide from the same man, but they were largely frustrated by a Watford side who doubled their lead before the interval.
Bond was the first to Alex Mowatt's free-kick and, as Leeds pondered, Hector Bellerin raced away on a thrilling counter-attack which was finished, admittedly in a stumbling fashion, by Battocchio for a fine second.
Leeds started the second half knowing it was nearly two years since they had overturned a 2-0 deficit and Smith wasted two chances to start a comeback inside a minute with two off-target headers, the second of which appeared easier to score.
He was bailed out by Pugh, though, who did score in the 50th minute, beating Bond from the tightest of angles from the left of the six-yard box after McCormack's cross was not dealt with and was allowed to reach the back post.
Watford appeared to be struggling to live with Leeds' renewed enthusiasm and eight minutes later Smith found his range to punish them. Lee Peltier robbed Anya in midfield, released McCormack and all Smith had to do was nod his cross in from two yards.
The visitors had no answer to a barrage of attacks and Bond was soon called into action again as he produced a fine stop to deny Austin from a yard and then dragged a vicious Murphy corner out from under his bar. The drama continued as a deflected Mowatt shot cracked the bar.
A third appeared to be on the cards for Leeds and McCormack thought he had it with a glancing header only to look up and see the linesman's flag raised, but he had no such worries later as he took in a long Murphy pass and slipped it past the advancing Bond for his 16th goal of the season and 10th in seven games.
But there was little time for Leeds to enjoy the moment as Deeney stayed alert to tuck in as Kenny took longer than expected to get to his feet after denying Thorne, while Watford would have won it had Marius Zaliukas not produced a fine block to keep out Joel Ekstrand with seconds left.