Davies was sent off for dissent in the 50th minute by Aussie referee Matthew Rossleigh and Nelmes was sent for an early bath near the end for throwing a punch.
At the same time Oldham full-back Luke Hooley was sin-binned for tripping, leaving ten-man Roughyeds to exit the field to a standing ovation after keeping the Bulls scoreless for nearly 50 minutes despite their numerical handicap.
Roughyeds' battle to make the play-offs now goes to the last weekend of the season and they will take heart from 'nilling' top-two opposition in the second half on consecutive Sundays.
If they win at London Skolars next Saturday and Whitehaven lose at title-chasing York City Knights 24 hours later, Scott Naylor's men will clinch fifth place and a play-off test at Bradford.
