Max Wright and Ben Davies scored the vital goals either side of Joe ironside’s finish.
And after demanding better from his squad last week, Elliott dished out the credit where it was due.
“It was all about the players today to show that courage and resilience,” he said.
“We knew we’d have to defend today, but I’m proud of them all, they all put a shift in.
“We deserved the win.
“I’m pleased for Max and a goal gets him going in the right direction.”
The contest finished with a scuffle in the tunnel involving Boston’s Ryan Qualter and Harriers defender Lee Vaughan.
Elliott confirmed referee James bell had taken no further action.
He added: “Ryan’s had a bit of verbals with their player and he’s gone past him. I’ve seen their player run after him and get involved.
“It’s something of nothing. It’s all been dealt with.”
Elliott also confirmed that Nicky Walker was omitted from the starting XI due to injury.
“Nicky’s injured,” he said.
“He’s done the warm up but didn’t feel fit enough to go on the pitch. We could have done with him.”