The dominant Wembley victory leaves England at the top of their Nations League group and secures them automatic promotion to League A.
Harry Kane opened the scoring to break the deadlock in the second half, giving England the lead from the spot after Jude Bellingham was brought down by Liam Scales in the box.
Scales, the Celtic defender, was handed a second yellow for the foul as Ireland were left to play the remaining 40 minutes with just ten players on the pitch.
The next five minutes saw another two goals added through Anthony Gordon - his first in an England shirt - and then Conor Gallagher.
Gordon managed to get on the end of a deflected cross from Newcastle teammate Tino Livramento, volleying in his first international goal.
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Gallagher then capitalised on the dwindled Ireland side yet again, prodding in at the back post following Marc Guehi's deflected header.
Shortly after, Carsley's substitutions made an impact with West Ham's Jarrod Bowen holding out for just thirty second before thumping a well-worked free kick pass into the back of the net on his first touch.
The debutant's were the gift that kept on giving on Sunday evening too, with Southampton's Taylor Harwood-Bellis adding a fifth through a powerful header from Bellingham's ball into the box.
It's a performance that leaves Carsley departing the interim role on a high, having beaten Greece 3-0 on Thursday night too.
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Carsley's England have scored 16 goals in six games, with eight players making their debuts, leaving Thomas Tuchel in a strong position to take over the job in January.
Through the goals from Gordon, Gallagher, Bowen, and Harwood-Bellis, it is the first time since October 1930 in which four players scored their first ever England goal in the same game.
The last fixture this occurred in was against Northern Ireland, with Harry Burgess, Jimmy Hampson, Sammy Crooks and Eric Houghton all on the scoresheet.
England now top their Nations League group due to their superior goal difference, despite Greece beating Finland 2-0 in Helsinki to match the Three Lions on points.
The standings leave England promoted into Group A, whilst Finland are relegated, after losing all of their matches in the competition.
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The result also sees England make some history with the Three Lions securing a third straight victory over the Irish for the first time ever having beaten them 2-0 in September and 3-0 in November 2020.
The first showdown between the two nations came in September 1946.