The 21-year-old, who was loaned back to the club where had had such a successful time last season on Friday, had seen ex-Hatters midfielder Lawson D’Ath put the Glovers ahead on 11 minutes, his first goal since November 2019.
Bromley equalised midway through the half through George Alexander as the scores were level at the interval.
With 20 minutes to go in the second period, Neufville was introduced and he made an instant impact, finding Tom Knowles to restore the lead.
Former Aston Villa and Crystal Palace youngster Williams elated to make his full Hatters debut in Carabao Cup
Jones could loan out Muskwe and Mendes Gomes as he admits certain players would have left regardless of cup exit
Jones still keen on pushing for defensive signing ahead of deadline day
Hatters were aware of McAtee's shoulder injury before agreeing to sign Grimsby striker
Luton boss will make a late decision in the transfer window on whether to loan out Pereira
The attacker, on his birthday, also went close to a third, but Bromley couldn't reply as the Glovers are now 13th in the table.
Neufville had made his first senior appearance since May 2021 during Yeovil’s 2-0 National League win at Dover Athletic on Saturday, coming on for the final 15 minutes as the Glovers ended a run of nine games without a victory.
Town attacker Elliot Lee came off the bench for the final nine minutes as Charlton beat Burton Albion 2-0 in League One on Saturday.
Forward Dion Pereira made his third successive start but Bradford City had their two game winning run ended with a 2-1 home defeat against Port Vale in League Two.
The visitors had led just after half time, Ben Garrity scoring, before James Wilson swiftly made it 2-0.
With 20 minutes to go, Pereira teed up sub Charles Vernam to halve the deficit, but Mark Hughes' side couldn't find a late equaliser.
Sam Beckwith played for an hour as Maidenhead United lost 1-0 at Chesterfield in the National League on Saturday, Akwasi Asante scoring the winner on 76 minutes.
However, he wasn't involved as the Magpies beat Southend United 2-1 on Tuesday night.
Defender Avan Jones had the final 10 minutes as St Albans City lost 1-0 at home to Ebbsfleet in National League South on Saturday
He also came on during Tuesday night's 2-1 defeat at Concord Rovers, replacing ex-Luton youngster Zane Banton, who had scored the Saints goal in the first half.
Midfielder Casey Pettit had 90 minutes as Lewes lost 1-0 to a last-gasp goal by Bishop's Stortford in their Isthmian League Premier Division match.
Winger Ben Stevens was an unused substitute in Hitchin Town's 2-0 Southern Premier Division win over Rushall Olympic at the weekend.