Rotherham were handed a half chance after two minutes winning a free-kick on the edge of the United area but Paul McLaren squandered the opportunity slamming the ball high over the target before Andy Monkhouse saw his low strike snuffed out by Phil Barnes.
United had to wait until the 32nd minute for their first real opportunity.
Midfielder Michael Tonge, in space on the left flank, weaved through the Rotherham defence and picked out Shaw but from six yards the United striker scuffed his shot.
Alan Quinn tried his luck with a shot on the turn from 18 yards but stabbed the ball over the bar before United snatched the lead in the 51st minute.
Shaw, who had a loan spell at Rotherham earlier in the season, struck after Scott Minto failed to cut out a through ball and the bald header striker coolly slotted past the advancing Mike Pollitt from 10 yards for his seventh of the season.
Substitute Luke Beckett, recalled from a loan spell at Huddersfield where he has scored six in seven games, almost hit the target with his first touch.
Tonge's looping strike came off the bar as Beckett produced a close-range header which was stopped on the line by the Rotherham keeper.
Monkhouse went close with a dipping free-kick which was tipped over the bar by Barnes before substitute Steve Kabba, playing his first game for 14 months after breaking a leg , almost grabbed a second in injury time with a strike from 18 yards.