Northern Ireland had sailed into a two-goal lead inside 50 minutes at Mourneview Park before the Royals striker scored twice from the penalty spot to earn Don Givens' side a share of the spoils.
Doyle's first spot-kick on 63 minutes was saved by Northern Ireland keeper Michael McGovern but the Royals striker slotted home the rebound.
And, on 76 minutes Doyle made no mistake from 12 yards to earn an unlikely draw for the Republic of Ireland.