Town returned to winning ways and increased the gap between themselves and the League One drop zone to six points after a first league win in nine games.
Tom Bloxham and Matthew Pennington scored the goals in both halves for the visitors from Cotterill, who were backed by 928 amid a 3,200 gate in Staffordshire.
Salop fans had their voices heard all afternoon as they roared their side for a second away league win of the season.
“They made a lot of noise, it was really good of them, it’s great when you have a big crowd away from home,” boss Cotterill said of the Pirelli Stadium backing.
“They support the team, sing behind the team and drive the team forward.
“I don’t know if the supporters of a club know the energy they can give to the players and what they create for the players.
“I think it’s so, so important. Look at the first game (Premier League), Leeds United – the support these players are receiving, regardless of the score, is incredible.
“Our boys, girls, ladies and gentlemen were fantastic even when the game was 0-0, because it’s a tough old game here, they were amazing.
“I said the other week that I thought they were brilliant and they were. We want to send them home happy every Saturday and Tuesday night.
“We play every game to win, sometimes you’re not good enough to win so don’t get beaten that day. There’s a good atmosphere and a good spirit, having as many fans as we had trips is great.
A busy period continues for Cotterill’s men with the toughest prospect of the season just around the corner against runaway leaders Rotherham at home tomorrow. Town, 17th, have yet to face the Millers twice this season.
The talented Shrews Bloxham teenager, 18, meanwhile won a stunning final for his second league goal of the campaign – and first since August – and fifth of the season in all competitions.
He was part of Cotterill’s three-man attack after an impressive display against Portsmouth in last week’s defeat and again caught the eye.
“There won’t be anyone in my team or any of the players who will be surprised that Tom scores that goal because he has that in him, his natural ability,” the manager said.
“But he needs to do it more regularly and understand the other side of the game, where he should be out of possession, so when we get him back he’s in a great position to go attacking.
“He’s had a lot in him in such a short time, I don’t think he’ll absorb it all until the summer, that’s when it all falls into place because every game is tactically different.”