And boos rang out around the ground when he substituted Easter and Richard Chaplow shortly after Vaughan's winner.
It could have been a lot different had Easter's early strike not been disallowed after referee Oliver Langford spotted a handball by Morison.
Huddersfield could have had a first-half lead but Joel Lynch headed wide while Vaughan's attempted chip was stopped by Stephen Bywater.
Terriers goalkeeper Alex Smithies made an acrobatic save to keep out Morison moments before Vaughan's goal.
Millwall desperately tried to salvage a point in the dying minutes but Alan Dunne's shot was saved by Smithies while Nicky Bailey glanced an effort over the crossbar.
Millwall boss Steve Lomas:
"I am enjoying my time here. I could've stayed up in Scotland and settled there. But I wanted to come here and test myself and this is a real test.
"I am enjoying it, as perverse as that may seem, but you have to take stock when things aren't going well. I thought we kept going right to the very end, it gives me heart that the lads are going every step of the way.
"I'm sure if we keep performing like we did today we'll get our rewards. I thought that's the best we've played this season."
Huddersfield boss Mark Robins:
"We're not getting carried away, it's still very early days. It's good to get the points on the board as it gives us confidence.
"It was a decent performance. We withstood everything Millwall threw at us and it's not an easy place to come. I think they're having a difficult time at the minute with a new manager who's trying to impose his ideas on the players.
"I think he's finding it difficult and he needs support. I think Steve needs the fans' help to get a bit of stability as they have a good squad of players and they play some decent stuff."
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