Henry blasted the Lions into the lead with a spectacular free-kick and Trotter doubled the advantage with a tap-in before the interval.
Luciano Becchio pulled one back for Leeds early in the second half, but Wales striker Morison made the points safe before Andy O'Brien scored with the last kick of the match.
These two sides have become big rivals in recent years, having both made heavy weather of getting out of League One until they were eventually promoted last season.
They could be on course to meet in the play-offs again with Leeds' hopes of automatic promotion fading fast.
The opening stages at a raucous, sold-out Den were typically scrappy but Henry lit up the game with his superb strike after 24 minutes.
Jonathan Howson fouled Kevin Lisbie on the edge of the penalty area and Henry stepped up to powerfully curl the ball round the wall.
Leeds goalkeeper Kasper Schmeichel got a hand to the ball but could only help it into the net as Henry celebrated his fourth goal of the campaign.
And the shell-shocked visitors found themselves two down just six minutes later when Schmeichel failed to deal with Andros Townsend's corner and Trotter was able to flick the ball over the line from a couple of yards out.
Substitute Neil Harris, on for the injured Kevin Lisbie, almost grabbed a third moments later when he got a touch on Henry's free-kick but the ball flew wide.
Leeds tried to hit back before the interval but Becchio was denied by a superb block from Darren Ward as he attempted to tuck in Max Gradel's cross.
However, Becchio's luck turned five minutes after the interval when he got a toe onto Bradley Johnson's long cross and prodded the ball past David Forde.
Lions keeper Forde came to the hosts' rescue moments later when he pulled off a fine save to keep out Gradel's fierce shot.
And instead it was Millwall who grabbed the game's crucial fourth goal just after the hour mark.
Henry's initial shot was blocked and Morison beat Schmeichel to the loose ball, dinking it over the keeper and into the net.
Lions stalwart Harris could have piled on the misery for Leeds but he sent one effort wide and blazed another late chance over the top.
The hosts dozed off in injury-time when O'Brien converted Eric Lichaj's long throw but there was barely time to kick-off before the final whistle blew.
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