A brace from Matt Derbyshire and a superb free-kick from David Murphy put Blues 3-0 up at half-time.
Steve Morison missed a second-half penalty just after the break for the hosts before Cameron Jerome came off the bench to head home with his first touch to make it 4-0.
Millwall grabbed an injury-time consolation through substitute Danny Schofield but the gulf in class between the two sides was evident throughout and Blues fully deserved the win.
Blues boss Alex McLeish went into the match with one eye on the Carling Cup semi-final against West Ham next week, making seven changes from the team that beat Blackpool in midweek.
Suggestions in the opening stages were that the move had backfired, with Blues failing to take a grip on the match.
Millwall, who went into the match on the back of an eight-match unbeaten run, included 2004 FA Cup finalist Neil Harris in their starting XI and created the most pressure early on.
Winger Scott Barron, who had his head bandaged after an aerial clash with Nikola Zigic, created problems down the left and James Henry struck a 25-yard shot just wide of Maik Taylor's goal.
Danny Shittu tested Taylor with a header from Millwall's third corner in 10 minutes before Jack Smith dissected the away defence with a 40-yard ball but Lions top scorer Morison screwed his shot wide.
Millwall immediately paid for the miss when Blues broke the deadlock through Derbyshire.
Home goalkeeper David Forde rushed out to stop the former Blackburn man when he was played in down the right by Jean Beausejour, but he could not snatch the ball from the striker's feet and he coolly turned and chipped home from 20 yards.
Millwall were taken aback by the goal and it was 2-0 six minutes later when Murphy fired his curling shot perfectly inside Forde's near post from an 18-yard free-kick.
Millwall continued to wilt and almost went 3-0 down soon after when Forde parried Alexander Hleb's 25-yard free-kick straight into the path of Derbyshire but the ball was scrambled clear.
Referee Lee Probert waved away Craig Gardner's claims for a penalty two minutes later as Blues searched for a third.
Henry gave Blues a warning with a 30-yard volley that went just wide before Millwall thought they had scored but Morison's tap-in was ruled out for offside.
Blues continued to press and the third came on the stroke of half-time when the Lions defence backed off, allowing Gardner to put Derbyshire through and he made no mistake from eight yards, stabbing the ball over Forde.
Millwall should have put themselves back in the game straight after the break when Blues captain Scott Dann was adjudged to have pushed Henry in the penalty area but Taylor saved Morison's tame spot-kick.
Millwall boss Kenny Jackett looked for fresh inspiration from Schofield and veteran striker Kevin Lisbie but they failed to create any major chances.
Beausejour served the hosts with a reminder of Blues' supremacy as he surged past his marker before seeing his 20-yard strike crash onto the bar on the hour.
McLeish made his final two substitutions of the afternoon when Derbyshire and the largely anonymous Zigic came off for Jerome and Kevin Phillips.
Large parts of the home support headed for the exit when Jerome headed home substitute Keith Fahey's cross with his first touch to make it 4-0 with 18 minutes left.
Millwall defender Darren Ward came on for Shittu as the Blues fans chanted for a fifth.
The side almost obliged straight away when Jerome had a shot blocked inside the box and the ball fell to Gardner but he failed to hit the target while Forde was struggling to regain his footing on the line.
Ward put in a crucial tackle to deny Jerome after he raced through with five minutes left.
Substitute Schofield steadied himself in the box before firing past Taylor in injury time for a consolation goal but it was the away fans who went home the happiest after watching their side put in a clinical and morale-boosting performance.
