Cardiff were 15th in the Championship table when veteran boss McCarthy took over three weeks ago but after two draws and now three successive wins, they are within six points of the playoff places.
Only Brentford have won more points or scored more goals in the Championship since McCarthy has been at the Bluebirds helm.
However, Dominic Hyam's late consolation goal at the Cardiff City Stadium means that the Bluebirds have kept just one clean sheet in their last 14 matches.
At the other end of the pitch, the Welsh side are the fifth highest scorers in the Championship and only three players have netted more than frontman Moore.
Meanwhile, Luton are the division's fifth lowest scorers and have not netted more than once in a game so far in 2021.
Despite being in 15th, Nathan Jones's side are only three points behind Cardiff in seventh, emphasising how tight the mid-table pack in the Championship is right now.
It could be a vital week ahead for Luton, as after hosting the Bluebirds, they face Stoke City (10th) and Millwall (14th).
The Bedfordshire side have lost only one of their last eight league matches at Kenilworth Road but equally they have only won once in their four most recent home games.
Cardiff's 4-0 win over Luton in November stands as their biggest win of the season to date. The Hatters, meanwhile, have only beaten the Bluebirds once in their last seven attempts.
Luton Town Championship form: LWLLDW
Luton Town form (all competitions): WLLLDW
Cardiff City Championship form: LDDWWW
Jones could name an unchanged team after earning a win and a clean sheet against Birmingham.
January signings Tom Ince, Kal Naismith and Elijah Adebayo are all still looking for their first league starts for Luton but are likely to be called upon in the next few weeks as Jones seeks to increase his side's attacking output.
Jonny Williams is in contention to make his Cardiff debut, having picked up a knock in training soon after his deadline day move from Charlton Athletic.
Luton Town possible starting lineup:
Sluga; Pearson, Lockyer, Bradley, Potts; Rea; Cornick, Mpanzu, Dewsbury-Hall, Clark; Collins
Cardiff City possible starting lineup:
Phillips; Morrison, Flint, Nelson; Ng, Vaulks, Pack, Bennett; Wilson; Murphy, Moore
We say: Luton Town 1-2 Cardiff City
Cardiff are building momentum under McCarthy, and they will see this as another winnable game. Luton show plenty of encouraging signs but are too inconsistent and struggle in front of goal, and we are backing an away victory at Kenilworth Road.