Deane was applauded off the pitch when he was substituted four minutes from the end of an embarrassingly one-sided contest once Leeds had recovered from conceding a second-minute goal to Gareth Ainsworth.
Leeds were unchanged for the third successive match, while Rangers had Marc Bircham back in midfield after suspension and Kevin McLeod returning on the left flank.
Kevin Blackwell's team showed a massive improvement on their last home game against Burnley when they were booed off the field, but they trailed after just one minute and 39 seconds.
In the opening moments, Kevin Gallen gave Gareth Ainsworth the chance to take on Danny Pugh, and the winger skipped past the full-back and beat Neil Sullivan from all of 20 yards. But The Whites bounced back to seize the lead with two goals in four minutes.
Healy equalised on nine minutes, cleverly chipping keeper Chris Day after Deane had headed down Gary Kelly's long ball.
Then it was Deane's turn to score, stabbing the ball home at the far post after Simon Walton's neat back heel found Wright in the box.
On 17 minutes Deane had the ball in the net again after Day spilled John Oster's skidding shot, but he was flagged offside.
Leeds were rampant and when Rangers defender Georges Santos nodded the ball straight into Wright's path, he accepted the gift and fired in his second goal in as many home games.
Gallen almost snatched a goal back, shooting inches wide from 25 yards as Rangers looked to repair the damage.
However, United moved further in front after 42 minutes when Deane finished from close range after good work by Wright.
Leeds were unstoppable and when Gary Kelly crossed from the touchline two minutes later, Deane was there again at the far post to chest down and shoot home his hat-trick and Leeds' fifth.
Rangers responded by replacing Jamie Cureton and McLeod with Marcus Bean and Lee Cook at the start of the second half, but Leeds soon had a chance for a sixth.
However, Day saved Healy's penalty after Danny Shittu brought down Walton, but it mattered little as Deane tucked away his fourth after 72 minutes.