The resurgent Lions are now unbeaten in five matches, a run aided by the fine form of striker Henderson, who has scored six goals in the last three games.
He netted twice after the break, with Liam Feeney adding the third, as the hosts piled further misery on their lowly visitors, who remain in the relegation zone.
Kenny Jackett unsurprisingly stuck with the same side which recorded comfortable wins over Leicester and Ipswich, while the visitors made three changes, with James McPake, Richard Wood and Gary Deegan handed starts.
Henderson had an early chance to open the scoring but his looping header from Feeney's cross drifted just over.
Reading loanee Brian Howard spurned two good opportunities to apply further pressure on the visitors' defence as his first corner was easily cleared behind by Cody McDonald before Joe Murphy confidently claimed the second.
Andy Thorn's men showed little adventure in possession but there was more than a hint of ambition about Carl Baker's 25-yard drive which stung the palms of David Forde on 13 minutes.
The hosts were content to let the Sky Blues keep the ball in their own half and sat back, waiting for an opportune moment to spring forward.
Such a moment came midway through the half when Jay Simpson seized on a loose ball on halfway and fed it between the Coventry defence, only for Murphy to race out to deny Henderson.
The home crowd cranked up the noise levels when Alan Dunne's left-footed drive from the edge of the box forced a brave block from Nathan Cameron, but from the resulting corner Coventry broke away and created their best chance.
Forde failed to deal with an awkward delivery into the six-yard box and McDonald pounced on the Irishman's fumble but powered his shot over the bar.
Jimmy Abdou could have ended his 103-game run without a goal just before the break but understandably lacked a little composure when presented with the opportunity to shoot from 12 yards, Richard Keogh comfortably recovering to block the defender's delayed shot.
Jackett introduced James Henry on the right wing for the second half, with the disappointing Howard making way as the hosts sought to up the tempo.
It was from the opposite flank that they created the opener after 53 minutes. Liam Trotter raced onto a long ball forward and advanced unopposed before feeding Henderson, who made no mistake from 12 yards out.
Staring down the barrel of their fourth game without a win and their seventh defeat of the season, Coventry almost hit back on the hour mark but McDonald headed Baker's precise free-kick wide from the heart of the penalty area.
Henderson made the points safe with a carbon-copy effort as he collected the ball from Trotter and lashed home in the 68th minute for his eighth of the season.
Feeney added the gloss as the Lions made it 10 goals in three games and underlined why the Sky Blues have not won at Millwall since 1955. Of more imminent concern for Thorn is the fact they remain winless on the road this season.
Jackett's charges, however, are finally looking up after a 10-game winless run threatened to destroy their season before it had even begun. On recent form, they may yet trouble the play-off places.