Leeds manager Jesse Marsch said he was "excited" to see his players "emerge from a tough moment" against fellow strugglers Watford to take a huge step towards Premier League safety.
Raphinha's fierce left-footed strike from the edge of the area gave the visitors the lead after the Hornets had twice gone close through Imran Louza and Cucho Hernandez.
Ismaila Sarr squandered a golden opportunity to fire Watford level in the second half, before Rodrigo capitalised on a dreadful mix-up between Hassane Kamara and Samir to double the visitors' advantage.
Leeds compounded Watford's misery when Jack Harrison beat Ben Foster with a powerful shot into the far corner to complete the scoring.
"The points are massive for us and there's confidence and momentum in the group," said Marsch, whose side have now collected 10 points from a possible 12 in the league. "We can see that the form of many players and the overall mentality of the group has grown so much.
"That's really helped us get to where we are right now."
The result lifts Leeds nine points clear of the relegation zone - although they have played three games more than 18th-placed Burnley, who travel to bottom club Norwich on Sunday.
"It's been a real pleasure to be their coach," Marsch told BBC Match of the Day. "[The players] are obviously hungry to stay in the league, but they are hungry to try to develop and get better and be the best they can be.
"Every day we're talking about some new topics and trying to fine-tune a lot of the principles we want to put in place. We have to keep going."
Watford manager Roy Hodgson will have taken heart from his side's spirited display against Liverpool last weekend but, as was the case at Anfield, the Hornets were undone by poor finishing against the Whites and now find themselves six points adrift of safety with seven matches left to play.
They had the better chances before Raphinha's well-taken opener, Louza sending a curling free-kick inches wide before Illan Meslier got his fingertips to Hernandez's inswinging cross-shot from the left.
Sarr was also thwarted by Meslier after racing on to Emmanuel Dennis' raking pass, but his effort would not have counted as he was in an offside position.
The Senegal winger missed an even better opportunity in the second half with the score at 1-0, sending a wild strike past Meslier's left-hand post - an effort which sums up Watford's plight.
Hodgson will be furious at the manner of Leeds' second goal, as Kamara's attempted clearance was deflected into Rodrigo's path by Samir, allowing the Spaniard to round Foster and calmly slide into an empty net.
The visitors, who kept their first clean sheet in 18 Premier League matches at Vicarage Road, put the seal on a vital victory five minutes from time when Harrison drilled an unstoppable shot past Foster for his third goal in as many games.
The win puts Leeds within touching distance of safety, but Watford's prospects look bleak after slipping to a ninth consecutive home defeat.
With trips to Crystal Palace, Manchester City and Chelsea still to come before the end of the season, the Hornets will need to improve their tally of seven points out of a possible 45 at Vicarage Road this term to stand any chance of avoiding the drop.
"I don't think the challenge has altered enormously," Hodgson said afterwards. "That's a few more points that we could have had that we haven't taken, but there are seven games left - four of them at home - and the players have got to find a way of putting this game behind them.
"They haven't lost by playing particularly badly, they've lost because the other team took their chances and now we have to get back in the right frame of mind for Brentford [next Saturday]."