Don Hutchison, signed on a six-month contract from West Ham, hit a glorious equaliser for the Lions but Healy had the last word with his second-half penalty.
Leeds had Eddie Lewis, Dan Harding and Robbie Blake making their debuts, while Millwall, who lost five key players in the summer, had Jamie Vincent and Hutchison making their first starts.
Millwall fans boycotted the game en masse in response to Leeds' insistence that they travel by coach in organised parties.
The Londoners survived by the skin of their teeth when Lewis drove fractionally wide from an early golden chance but the American winger made amends in the 28th minute with an in-swinging corner which arrived inside the six-yard box for Healy to volley cleverly over his shoulder and score the first goal at Elland Road this season.
Barry Hayles was left isolated in the Mllwall attack, with Paul Butler and Sean Gregan composed at the heart of Leeds' defence.
Former Leeds midfielder Jody Morris, who scored from the penalty box in this fixture last season, was booed whenever he touched the ball but he was the innocent party when Shaun Derry and Eirik Bakke caught him with late tackles which should have earned bookings.
Leeds played the neater football and Bakke, who made his first start for 18 months, was unlucky not to score when Andy Marshall saved his close-range shot at the second attempt in the 53rd minute.
However, Millwall snatched a shock equaliser when Harding made a weak tackle, enabling Alan Dunne to play in Hutchison whose rising shot from just inside the penalty box gave Neil Sullivan no hope.
Leeds scored the winner with 17 minutes left when Bakke was brought down by Marvin Elliott, and Healy powered home the penalty.