Rotherham's new owners had invited Gazza to make a half-time prize draw and sparked speculation he was about to be named manager.
But Gazza was asked to stay away at the last minute amid fears fans could give him a hostile reception – and Moore, under pressure for the first time in his seven-year reign, was given a hero's welcome.
Plymouth boss Bobby Williamson was also given a rousing reception marking his achievement as a Rotherham striker in the 1980s when he scored 49 goals in two seasons.
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Plymouth's best early chances came when Lee Makel crashed an ambitious shot wide and Mick Evans hit a first-time effort over.
But it was Plymouth who grabbed the winner in the 65th minute with a header from Matt Doumbe. Lee Makel's deep free-kick was headed across goal as Rotherham keeper Mike Pollitt flapped and Doumbe nodded into the open net.
Rotherham bounced back and defender Paul Hurst almost leveled with a curling free-kick that drifted just wide of the goal. Rotherham centre-back Swailes was in the area to pounce after a corner was parried by the keeper but fired his shot wide. David Norris might have added a second for Plymouth but as he raced in on goal Pollitt blocked him superbly.