The 19-year-old had been kept in check as Rotherham fell two goals behind and seemed destined for defeat.
But an own goal by former Sheffield Wednesday youngster Rory McArdle gave Rotherham hope with 13 minutes left although time had almost run ou
t when Reid struck. Stoppage time was in its fourth minute when Reid controlled a loose ball before lifting a volley beyond the goalkeeper.
Then he went extremely close to winning it, sending a close-range header a fraction wide in the final move of the match.
"He said before the game he was going to score twice but we're just glad he managed one," said Rotherham manager Mark Robins. "He can always hurt teams and do what he did but there's more to come from him and you have to look overall and ask if he's given us enough throughout the game."
After Rotherham started brightly, Rochdale took over.
Jordan Rhodes marked the start of his loan spell from Ipswich with the opener four minutes before half-time. Then youngster Will Buckley netted early in the second half.
Rochdale substitute Lee Thorpe was sent off following a two-footed challenge on Ian Sharps to aid Rotherham's bid.
Rotherham United: Warrington; Lynch, Sharps, Fenton, Nicholas; Harrison (Cummins 64), Mills, Hudson (Rhodes 70); Reid, Taylor (Broughton 46), Burchill. Unused substitutes: Cann, Green.
Rochdale: Russell; Ramsden, Stanton, McArdle, Kennedy; Buckley (Toner 72), G Jones, Keltie, Rundle; Le Fondre (Thorpe 65), Rhodes (Dagnall 81). Unused substitutes: M Jones, Wiseman.
Referee: D Drysdale (Lincs).
Man of the match: Ian Sharps.
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