The hosts initially struggled to make inroads against 11 men, but an early red card in the second half triggered an England onslaught, as Harry Kane stroked home the opener from 12 yards before Anthony Gordon, Conor Gallagher, Jarrod Bowen and Taylor Harwood-Bellis all scored their first senior goals for their country.
As expected, the departing Carsley recalled captain Kane to the England XI in the capital, but the Bayern Munich forward could not repeat Ollie Watkins's seven-minute trick against Greece and was frustrated alongside the rest of his teammates in the first 45.
The hosts had nearly three-quarters of the ball and fired eight shots on the Ireland goal in the first half, but not a single one of them found its way through to Caoimhin Kelleher, who was being guarded expertly by his defence.
Heimir Hallgrimsson's side were also showing a bit of intent on the counter-attack and should have been the happier outfit at half time, but that all changed early in the second half, when Liam Scales was sent off for a foul on Jude Bellingham and Kane did the rest from 12 yards.
With one of their defensive rocks sent for an early bath, Ireland's defensive game plan collapsed, and Carsley's rampant troops put the result beyond any doubt within a matter of minutes as Gordon and Gallagher - both netting their first England goals - also struck before the hour mark.
The first-time scorers were out in force at Wembley, as two more players waiting to open their England accounts - Bowen and the uncapped Harwood-Bellis - also breached a beleaguered Ireland backline to give Carsley the most perfect of perfect send-offs.
Even though Greece also beat Finland in their last League B Group 2 match, the Three Lions' superior head-to-head goals record means that they will shoot straight back up to League A without the need of a playoff, but Ireland must take part in a two-legged tie next spring to salvage their second-tier status.
ENGLAND VS. IRELAND HIGHLIGHTS
Harry Kane penalty goal vs. Ireland (53rd min, England 1-0 Ireland)
Ireland's dogged work in the first 45 minutes is rendered meaningless in the first eight minutes of the second half, as Kane fizzes in a gorgeous ball into the box for Bellingham, who checks back and is felled by an already-booked Scales.
The Ireland defender takes the walk of shame for a second yellow-card offence, and Kane takes a stuttered run-up before coolly sending Kelleher the wrong way from the penalty spot.
Anthony Gordon goal vs. Ireland (56th min, England 2-0 Ireland)
The complexion of this game has changed in an instant, and this one is all about the Magpies.
Full debutant Tino Livramento delivers a rather poor cross from the right, but Nathan Collins and Josh Cullen make a meal of trying to clear their lines, and the ball comes through to Gordon to sweep home a first England goal into the bottom corner.
Conor Gallagher goal vs. Ireland (58th min, England 3-0 Ireland)
Fair to say that the Scales red card well and truly opened the floodgates for England.
Again, Ireland fail to deal with a cross from the right - this time from a Noni Madueke corner, which Marc Guehi heads on to Gallagher to crash home at the back stick for his maiden England goal.
Jarrod Bowen goal vs. Ireland (76th min, England 4-0 Ireland)
How about that for a first touch!
Only on the pitch for a matter of seconds, substitute Bowen makes a smart run to the edge of the box to meet Bellingham's short set-piece, and the West Ham United winger fires a crisp first-time strike through a sea of bodies and into the back of the net.
Taylor Harwood-Bellis goal vs. Ireland (79th min, England 5-0 Ireland)
You get a first England goal, you get a first England goal, everybody gets a first England goal!
Debutant Harwood-Bellis is the latest to wheel away in celebration after opening their Three Lions account, meeting Bellingham's cross with a terrific header into the far corner past Kelleher's futile reach.
MAN OF THE MATCH - JUDE BELLINGHAM
As Carsley and England's first-time goalscorers lap up the post-game fanfare, Bellingham's display may go slightly under the radar, but the Real Madrid star proved that class is permanent amid his downturn in fortunes in the Spanish capital.
After his nifty footwork won England their deadlock-breaking penalty, Bellingham laid on the assists for Bowen and Harwood-Bellis's maiden England goals; the only thing that was missing was a goal.
ENGLAND VS. IRELAND MATCH STATS
Possession: England 74%-26% Ireland
Shots: England 22-1 Ireland
Shots on target: England 7-1 Ireland
Corners: England 12-0 Ireland
Fouls: England 7-9 Ireland
BEST STATS
WHAT NEXT?
Carsley and Thomas Tuchel will now conduct the official handover process, before the latter assumes office in January and takes charge for the first time during the opening round of World Cup qualifiers in March; the group draw will be held on December 13.
As for third-placed Ireland, the Boys in Green will have to face one of the runners-up from League C to avoid relegation to the Nations League's third tier; the draw for the playoffs will take place on Friday before the first leg on March 20 and second on March 23.