This victory kept up Boston's fine run of form since Elliott joined the club, writes Tom Feaheny.
They are now just five points off the play-off places.
"It is always difficult against the team at the bottom, you are expected to win but we handled the pressure," Elliott told the club's website.
"The fast start getting the early goal was excellent, then we were superb during the first-half, the tempo and movement was great.
"It was disappointing not to get a clean sheet, the penalty we gave away was one, but we move away from that and focus on the win.
"We are getting goals from all different types of areas, and that is important."
For more news, reaction and action from across the National League, like us on Facebook and follow us on Twitter and Instagram.