Fresh from the FA Cup defeat of Peterborough, the victory lifted Nigel Clough's bouyant team further away from the relegation zone, but left a question mark over caretaker Simon Wormull's hopes of landing the vacant manager's post at Crawley.
Conditions underfoot were tricky, with half the pitch in the shade of the main stand heavily frosted.
Both teams struggled to play with any fluency and, unsurprisingly, the opening goal stemmed from a mistake when Shaun Harrad fastened onto a stray backpass by Neil Jenkins and steadied himself before drilling home a low shot from 15 yards in the 13th minute.
Crawley went desperately close to levelling the scores during their best spell of pressure midway through the first half.
A partial clearance by Jake Sedgemore fell invitingly for Paul Armstrong, but his fierce left-foot volley from just inside the area hit the inside of a post and ran across the face of the goal before the ball was scrambled away by Ryan Austin.
Neither goal was seriously threatened again before the interval, with Burton keeper Saul Deeney easily dealing with shots from Daryl Clare and Wormull while home skipper Darren Stride was unable to keep down his eight-yard header after good work by Chris Hall.
Clear-cut chances continued to be at a premium until the game came to life in the final 15 minutes.
Burton doubled their lead in the 75th minute thanks to the sheer persistence of substitute Andy Corbett.
Corbett managed to keep the ball in play and skip past Ian Simpemba close to a corner flag and pulled it back for Shaw to smash home a 12-yard shot off the underside of the crossbar.
Clare threw the Reds a lifeline two minutes later with an adept left-foot finish after Wormull's ball into the box eluded the Burton defence - the first goal conceded by Clough's men in six games.
But Corbett and Shaw had the final say as Burton sealed their victory in the 88th minute.
Corbett spearheaded a terrific breakaway attack and unselfishly squared the ball for Shaw to tap in his eighth goal of the season.
Conditions underfoot were tricky, with half the pitch in the shade of the main stand heavily frosted.
Both teams struggled to play with any fluency and, unsurprisingly, the opening goal stemmed from a mistake when Shaun Harrad fastened onto a stray backpass by Neil Jenkins and steadied himself before drilling home a low shot from 15 yards in the 13th minute.
Crawley went desperately close to levelling the scores during their best spell of pressure midway through the first half.
A partial clearance by Jake Sedgemore fell invitingly for Paul Armstrong, but his fierce left-foot volley from just inside the area hit the inside of a post and ran across the face of the goal before the ball was scrambled away by Ryan Austin.
Neither goal was seriously threatened again before the interval, with Burton keeper Saul Deeney easily dealing with shots from Daryl Clare and Wormull while home skipper Darren Stride was unable to keep down his eight-yard header after good work by Chris Hall.
Clear-cut chances continued to be at a premium until the game came to life in the final 15 minutes.
Burton doubled their lead in the 75th minute thanks to the sheer persistence of substitute Andy Corbett.
Corbett managed to keep the ball in play and skip past Ian Simpemba close to a corner flag and pulled it back for Shaw to smash home a 12-yard shot off the underside of the crossbar.
Clare threw the Reds a lifeline two minutes later with an adept left-foot finish after Wormull's ball into the box eluded the Burton defence - the first goal conceded by Clough's men in six games.
But Corbett and Shaw had the final say as Burton sealed their victory in the 88th minute.
Corbett spearheaded a terrific breakaway attack and unselfishly squared the ball for Shaw to tap in his eighth goal of the season.