Harris named an unchanged starting XI for the fifth successive match, including four Academy graduates, whilst there was not a solitary Bournemouth player from their epic 3-3 midweek draw with Arsenal in a side that showed 11 changes.
The virtue of fielding a settled side was clear for all to see as Millwall set about their task with an air of confidence and composure about their play.
A few early back passes were adequately dealt with by Cherries keeper Adam Federici under pressure from The Lions' front men. However, with five minutes on the clock Lee Gregory timed his interception of a back pass to perfection and slid in to nick the ball from the reach of the keeper. Morison was on hand to pick up possession but his shot bobbled agonisingly wide for a goal-kick.
Moments later Shaun Williams slipped the ball through to Gregory, who had escaped his marker and was one on one with Federici. The striker steered his effort inches wide of the upright
The Lions were full of energy and enterprise, making it difficult for Bournemouth to get into any attacking rhythm and midfielder Ben Thompson, with options either side of him limited, took control just before the quarter hour mark, working an opening on the edge of the penalty area but lashed over.
Tyrone Mings was lucky to escape punishment on 17 minutes appearing to push Morison in the chest after both had got in a tangle battling for possession in the danger zone.
Cherries' left-back Brad Smith conjured the visitors' first clear chance on goal with 23 minutes on the clock. Jordan Ibe smuggled the ball to his team-mate just to the left of the 'D' but Smith hit a sizzler off the mark.
The Lions' first corner of the game came a couple of minutes later and was cleared behind at the back post by the boot of a Cherries defender.
There was no such let-off when Williams dinked over the resulting dead ball from the opposite flank, and Morison's superb header provided a perfect finish to hand Harris' men a 1-0 lead.
Millwall were close to doubling their lead 12 minutes before the break following a magnificent piece of play by Fred Onyedinma. Showing great determination and strength, Onyedinma dug in and won possession deep in his own half, then set off on a a mesmerising run the length of the pitch, picking off a handful of Cherries' players before sliding an inch perfect pass through to Gregory. Unfortunately the latter's finish was just off target, steering the ball a foot wide of the far post with the goal at his mercy.
The visitors responded and it took a great tackle from Byron Webster to deflect Ibe's shot for a corner following a quick counter attack.
Former Lion Lewis Grabban then saw his close-range effort deflected behind for a corner and Marc Pugh's 25-yarder flew high over the bar, but Millwall defended resolutely to take a slender lead in at the halfway stage.
Bournemouth introduced Callum Wilson for Jordan Lee at the start of the second-half, but it was The Lions who threatened first, Federici doing well to save the striker's angled drive at his near post.
The visitors spurned a glorious opportunity to level on 47 minutes when an unmarked Lys Mousset powered a header off target.
That miss proved to be costly and less than 90 seconds later, Federici was picking the ball out of the Bournemouth net for a second time. Morison's initial cross was parried by the keeper and Cummings was perfectly placed to bundle the ball over the line from close range for his first ever goal at The Den.
A thunderbolt from Grabban whistled wide as Bournemouth tried to work up a head of steam, but Millwall continued to push forward. A good advantage by referee Andrew Madley enabled a quick move down the left to progress after Gregory had been flattened by Dan Gosling and sub Shane Ferguson's angled drive flashed inches wide. Gosling was rightly booked for his cynical challenge when play resumed.
Onyedinma, who was here, there and everywhere with a super display, kept a calm head under pressure, and with the equally cool head of Cummings, the duo wriggled the ball out of their own penalty area as Bournemouth tried to pick a way through.
David Worrall was introduced with quarter of an hour remaining for Onyedinma, who received a standing ovation for his excellent shift.
With the minutes ticking away Bournemouth had no option but to go for broke or face the embarrassment of defeat at the hands of a team two divisions below.
However, having worked so hard to gain a two-goal cushion Millwall dug in, blocking, tackling, chasing and making life as uncomfortable for Bournemouth as possible all over the pitch.
Eddie Howe's men were restricted to shooting from distance with efforts from Ibe and Pugh failing to test Jordan Archer in the home goal.
Morison could have put the icing on the cake with a third goal as the game approached the 90th-minute mark, leaving his marker for dead on the left and powering forward. With sub Calum Butcher available in the middle, Morison went for goal himself but fired off target.
Bournemouth did have the ball in the back of the net in injury-time when Wilson stabbed home after Archer had parried Pugh's shot, but the linesman's flag shot up to rule out the effort.
Millwall's response was swift, slick and stunning - a sublime pass from sub David Worrall picked out sub Ferguson on the left, he in turn skipped his way into the penalty area and arrowed a low shot into the bottom corner to crown an excellent afternoon's work.
See you in Round Four!