Right-back Darville scored just after the break with a 20-yard effort as a youthful Leeds side proved too much for Rotherham.
The club's second string have gathered 30 points from their last 10 fixtures and recorded clean sheets in every match bar one, and Neil Thompson's side are unbeaten since October.
Thompson selected a strong and experienced line-up when Leeds won a potential title decider against Huddersfield last week, with several first-team men in need of match fitness.
However, yesterday's team did not contain a single first-team player and featured two 16-year-olds.
Leeds Reserves: Edwards, Darville, Garbutt, Falkingham, Watson, Milne, Hatfield, S Jones, Elliott, Whitwell, McCann.