The Whites' 2-1 defeat to Arsenal on Sunday paved the way for Everton to climb clear of danger with a 2-1 win away at Leicester City, leaving United to fall below the dreaded dotted line into 18th place.
The Toffees now sit one point ahead of Leeds and Burnley and could better their advantage if they get a result against Watford, who are winless in five, when they play their game in hand on Wednesday evening.
The fight to remain in the Premier League now reads as a straight shootout between Jesse Marsch's side and the Clarets - which of the two teams can gain more points in the final three games of the season?
Former Whites centre-back Woodgate, who bagged more than 100 appearances for Leeds, says the outcome of the two-horse race is near-impossible to predict.
"I hope they do! It’s hard to judge," Woodgate said.
"Everton have been brilliant the last few games, beating Chelsea at home and beating Leicester away and the victory against Man United as well – I was looking at their away form and thinking they hadn’t won since Brighton on August 28th – six points away from home since before Leicester, and I think they’ll be okay now as they’ve got a couple of home games and I think they’ll pick up six points from their two home games. It’s gonna be down to Burnley and Leeds.
"I watched Jesse Marsch’s first game against Leicester, and I know they got beat in that game, but you could see what they were trying to do and they were very good. They’ve been playing very well, and I thought they were clear of the danger, but have been dragged back in by the form of Burnley and Everton. But it’s out of Burnley and Leeds!"
The first of Leeds' trio of vital Premier League games takes place on Wednesday evening, when third-placed Chelsea will visit Elland Road hoping to inch closer to Champions League qualification.
Woodgate believes that a draw is achievable against the Blues, who will also have half an eye on their upcoming FA Cup final against Liverpool.
"You wanna try and win every game but a point wouldn’t be a bad result against Chelsea," Woodgate told BritishGambler.co.uk."But if they rest a few players, Leeds could capitalise on it and Chelsea are not in great form at the minute - they’ve got five points from their last five games and look like they’ve taken their foot off the gas a bit, and have the cup final coming up so will they maybe rest a few players for that?
"I know third isn’t in the bag yet with Arsenal and Spurs putting the pressure on, so it will be interesting to see what team Thomas Tuchel puts out."
After an impressive maiden season in the top flight ended in a ninth-placed finish, the Whites' second Premier League campaign never really got off the ground, with United's struggles leading to the eventual sacking of former boss Marcelo Bielsa.
Though a string of difficult injuries have stunted the Whites' progress, Woodgate highlighted one thing that Leeds could have done differently to prevent the threat of relegation.
"Maybe Leeds could have brought in a big name striker in the January transfer window," Woodgate suggested.
"I think the injuries have really hampered them. Most of the season they’ve had no Cooper, Phillips and Bamford – the spine of the team. Cooper is injured now, Stuart Dallas, Bamford. Without three of the most reliable players aside from Phillips and Raphinha.
"It’s going to be really difficult for Leeds, but I just hope they stay up. I really do because they’ve a massive football club.
"I would have kept Bielsa on, as I think he would have turned it round. I know they’d been on a bad run, particularly at home losing a few, but he would have turned it around.
"I was a big fan of Marcelo Bielsa, and what he did to the Leeds team and the players, he improved the club and the players, but I just think Leeds wanted something fresh."