The home side were rocked by captain Wes Morgan's early dismissal, but held firm for 87 minutes before seeing their promotion hopes suffer another blow as their winless run extended to six matches.
Millwall were disappointingly conservative considering their numerical superiority, but took the spoils when Irishman Dunne popped up three minutes from time to slot home Richard Chaplow's cut-back.
Leicester's hopes of ending their barren run were dealt a severe blow after only three minutes when skipper Morgan clumsily bundled into Andy Keogh and, as the last man, left referee Stuart Attwell little choice but to send him off.
Kasper Schmeichel brilliantly kept out Shane Lowry's 20-yard effort from the subsequent free-kick, but Leicester reorganised effectively and had their fair share of chances in the first half.
Ritchie DeLaet's cross fell for Michael Keane, but his point-blank header was somehow scrambled off the line by Lowry.
At the other end Schmeichel was alert to tip Jermaine Easter's 20-yard drive behind for a corner, before a marauding run from inside his own half by Belgian DeLaet finished with Danny Shittu hacking the full-back's shot off the line.
Millwall had neither the attacking inclination nor creativity to make their numerical advantage tell and it was Leicester who threatened again when David Nugent burst down the right and flashed a powerful shot across goal.
Attwell's hopes of endearing himself to the home fans who felt aggrieved at his earlier decision went awry when he failed to spot Hulse control the ball with his hand inside the penalty area, but the former West Brom man was again denied by Schmeichel.
Hulse was not so lucky shortly after the half-hour mark though, when he converted Easter's low cross only to be ruled offside by assistant Wayne Barratt.
With chances at a premium after the interval the game quickly descended into a bad-tempered affair; Lions midfielder Liam Trotter particularly fortunate to escape with only a caution when he went in late on Jeff Schlupp.
The game looked to be petering out into a goalless draw when Chaplow, who had bossed proceedings for much of the night, found space down the left and although his pull-back missed all of the visiting forwards, Dunne timed his run forward to perfection to settle matters.