Brad Nicholson's header seven minutes before half-time sealed United's safe passage at the expense of their newly-promoted visitors.
United, led by the excellent Michael Bostwick, repelled plenty of Rushall pressure after the break, although keeper Cameron Gregory was not forced into a meaningful save.
“The aim was to get through the tie,” said United’s assistant manager.
“The first half we controlled the game really well. The second half, they made it difficult and it became a fight. We went away from doing things we wanted to do.
“The two centre halves were magnificent, they won every ball in there. We knew everything would be inn the air. We have come unstuck with this type of game this season but today we dealt with it and kept a clear sheet. The fans go home happy.
“We will just keep trying to push as far as we can.
“Curzon will be tough but confidence will be growing with the group.
“We showed we have got the ugly side to us and hopefully we can continue keeping clean sheets.”
Midfielder Jordan Richards felt the win gives United a great chance to build as they look for further progress.
“We had a very good first half and moved the ball well,” he said. “The second half was tougher but we stood firm and rode it out.
“We defended very well and everyone was compacted, we had a good unitl and they didn't really create chances
“The two centre-halves were both very good and complemented each other very well, it was a very good performance
“We just want to keep the momentum going now and see where we end up. We have a few injuries but we have a few coming back as well.
“We have a chance to build on this next week. We are good at home, but we want to get better results away from home.”
Boston United's National League North fixture against Scunthorpe United will be re-arranged due to continued Emirates FA Cup involvement.