The Sunderland defender struck for just the second time in 93 internationals with 26 minutes gone at the Aviva Stadium after skipper Robbie Keane's penalty had cancelled out Dmitriy Shomko's 13th-minute rocket.
Shomko's 77th-minute own goal completed the scoring as interim manager Noel King was handed a win which ended a run of three successive qualifying defeats.
Reid might have got his own name on the scoresheet 15 minutes from time when he created space for himself on the edge of the box, but fired straight at the keeper.
It proved to be his last contribution as he was replaced to warm applause from a sparse crowd at the Aviva Stadium by Aiden McGeady seconds later.
The Spartak Moscow winger needed just two minutes to make his mark when he ran on to Stokes' back-heel and crossed into the six-yard box, where Shomko could only turn the ball into his own net under pressure from Kevin Doyle and Keane.
Stokes also received an ovation when he was replaced by Wes Hoolahan with three minutes remaining as a satisfactory evening drew to a close.
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