The superbly crafted first-half header from Shipperley and late strikes from McAnuff and Morgan were enough to earn the Dons the win and give home boss Ronnie Moore his worst week in charge at Millmoor with a hat trick of home defeats.
Two early saves from Rotherham keeper Mike Pollitt denied Wimbledon a flying start.
Just 35 seconds after the start Damien Francis lifted a smart ball for livewire David Connolly he poked an angled shot but Pollitt was sharp to dive low to his left and fingertip the ball out.
Then13 minutes in Shipperley flighted a clever cross for Connolly but the Irish international's header was well saved by Pollitt.
Rotherham then had the ball in the net with an Alan Lee header from John Mullin's corner but he was offside, but ten minutes before the break Wimbledon deservedly took the lead after the best move of the half.
Jermaine Darlington and Francis did well before Peter Hawkins produced a quality cross and Shipperley glanced in his 12th goal of the season at the near post.
Martin McIntosh produced an optimistic free kick from 20 yards five minutes into the second half but keeper Kelvin Davies coped comfortably and a sizzling break by Chris Sedgwick had Wimbledon in a panic until he overhit his cross.
But Lee was only a fraction away from a 54th minute equaliser when he made a powerful run on the right before cutting inside and driving a low shot out of reach of Davies, but it bobbled an inch wide of the post.
Then five minutes from the end McAnuff burst clear on the right with a 40-yard run before rifling in a super shot.
And in the dying seconds Morgan produced a carbon copy goal with a convincing run and shot.
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