Henry snatched victory deep in added time, the third game in a week that Huddersfield were denied by late goals.
The Terriers had been held by both Stockport County and Colchester United after last-gasp strikes and Henry all but ended their slim play-off hopes.
Marc Laird gave Millwall the lead in the 69th minute only for Gary Roberts to level five minutes later.
As the game entered the third minute of the four added by referee Oliver Langford the Lions snatched a lifeline.
The first half was a lack-lustre affair and the closest either side came to scoring was when Huddersfield defender Andy Butler headed against his own crossbar.
Millwall edged the opening period with a Gary Alexander free-kick going just over the top and the dangerous Dave Martin also going close.
Huddersfield failed to trouble David Forde in the Millwall goal.
The second-half introduction of veteran striker Andy Booth lifted the home side and Anthony Pilkington's deflected shot saw Forde called into action for the first time.
Huddersfield should have scored in the 53rd minute when Lionel Ainsworth beat Nadjim Abdou for pace but prodded wide.
Huddersfield defender Chris Lucketti had a header saved by Forde before Laird broke the deadlock. Martin pulled the ball back and Laird finished with a shot into the bottom corner of the net.
Millwall, with eight away wins under their belts before this game, were pegged back when Roberts fired home at the back post from Pilkington's deep cross.
Eleven minutes from time Huddersfield had young keeper Alex Smithies to thank for tipping Alexander's header onto the bar.
Huddersfield boss Lee Clark had warned his players not to fall victim to another late disaster, but sub Scott Barron sprinted clear from his own half after a Town corner routine had broken down.
He ran the length of the pitch and squared for Henry who turned the ball home to claim the points.