Full-time score from the Ricoh Arena
The Lions had been looking comfortable after taking a 19th-minute lead through defender Byron Webster, but were left playing over an hour of the game with 10 men after midfielder Shaun Williams was shown a straight red card for an off the ball incident with Sky Blues' Ruben Lameiras.
Two goals in eight second-half minutes from Coventry City's John Fleck and sub Marcus Tudgay sent Play-Off hopefuls Millwall spinning to defeat at the Ricoh Arena.
At the other end Sky Blues full-back Aaron Phillips saw a ferocious first-time volley from 20-yards flash a whisker wide of the upright as the home side conjured their first shot on goal in an even opening between the two teams.
Millwall, however, looked composed and assured in their play and a delightful 17th-minute move caused panic in the home defence again. Shane Ferguson threaded a sublime through ball to Morison, whose shot was closed down before Chris Taylor's follow-up was blocked for a corner.
Although Ferguson's resulting delivery came to nothing, The Lions' next corner produced the all-important first goal when Webster thundered home a powerful header from Taylor's delivery to give Charles-Cook no chance.
No sooner had Millwall got their noses in front than they found themselves reduced to 10 men following that rush of blood by Williams for an off-the-ball altercation with Lameiras, leaving Harris' men facing an hour of the match at a numerical disadvantage.
Harris brought on Jimmy Abdou for Ferguson with O'Brien switching to the left flank and Morison operating as a lone striker, whilst Coventry responded by replacing Romain Vincelot with James Maddison.
Coventry created a trio of decent chances before the break with Adam Armstrong twice firing wide from near identical positions 12 yards out and Andy Rose heading a Cole free-kick over the bar.
It was inevitably going to be a real battle for Millwall's 10 men, but expert defending from Webster with a timely interception from Phillips and a succession of strong headed clearances from central defensive partner Mark Beevers kept the Sky Blues at bay for the remainder of the opening half.
A tactical switch at the start of the second period saw Taylor and O'Brien switch flanks, operating on the left and right respectively but within nine minutes of the restart Sky Blues replaced Sam Ricketts with Tudgay as they adopted an all-out attacking policy.
Millwall could have doubled their tally just seconds after Tudgay's introduction when O'Brien failed to connect properly with the ball 14 yards out, but it fell kindly into the path of skipper Morison, whose drive rippled the side netting.
However, it was the home side who hauled themselves back onto level terms with a goal of real quality from Fleck, rifling an unstoppable 61st-minute shot into the top corner from 25 yards leaving keeper Archer grasping at thin air.
Coventry turned the game on its head and edged ahead with a second goal just eight minutes later when sub Tudgay capitalised on some hesitant defending to get his foot on the end of Cole's ball over the top and steer home from an acute angle.
Mowbray's men really had the bit between their teeth as The Lions were under siege from a home side now brimming with confidence and pushing on in search of a third, killer goal.
Millwall kept their shape - and their nerve - and so nearly conjured a second goal four minutes from time when Joe Martin's hooked shot dropped just over the bar moments before sub Ed Upson's drive flew inches off target.
Left-back Martin was denied a dramatic injury-time equaliser with a stinging first-time 20-yarder that was heading into the top corner until keeper Charles-Cook flung himself across goal and somehow got his hands to tip the ball round the post to compound Millwall's frustrations on an afternoon that had promised so much, but ended in bitter disappointment.
11,632 (away 1,862) Att:
Webster (19mins) Scorer:
Williams (27mins) Sending off:
Abdou (83mins), Webster (90+1min) Bookings:
Archer, Romeo, Martin, Beevers, Webster, Williams, Thompson, Ferguson (Abdou, 33mins), O'Brien (Upson, 58mins), Morison, Taylor (Gregory, 79mins). Subs not used: Forde, Craig, Philpot, Onyedinma. Millwall:
Fleck (61mins), Tudgay (69mins) Scorers:
Charles-Cook, Vincelot (Maddison, 36mins) Fleck, Lameiras (Lorentzson,84mins), Armstrong, Cole, Stephens, Rose, Phillips, Ricketts (Tudgay, 54mins), Martin. Subs not used: Addai, , Bigiriman, Murphy, Fortune. Coventry City: