Doyle, just 19, had only played one professional game for Chester and was making his debut for Forest with first-choice keeper Paul Gerrard ruled out through suspension.
But the teenage keeper had a game to forget after somehow allowing Jermain Defoe's free-kick to fall through his hands and gift Tottenham the opening goal on the stroke of half-time.
However, Taylor put aside his love for Spurs and ensured Doyle was not the villain of the day when he made the most of a mix-up in the Spurs defence and scored a crucial equaliser.
And it so easily could have been a lot worse for the Premiership side after Paul Robinson produced four wonder saves to keep his side in the competition.
Even though Forest are nine points adrift of safety at the foot of the table, Gary Megson's side could have broken the deadlock after just six minutes.
Kris Commons released defender Alan Rogers into the penalty box, but with just Robinson to beat, he scooped his shot over the crossbar.
Tottenham came close on 20 minutes when Fredi Kanoute picked out Michael Brown and he struck a curling 25-yard drive which produced a fine save from Doyle diving away to his left.
In an open encounter, Forest showed they were not just here to make up the numbers and forced a superb save from Robinson on 26 minutes.
Commons outpaced two home defenders before racing clear into the penalty box, but his low drive was superbly beaten out by the England keeper.
The home side almost produced a carbon copy of the goal they scored against West Brom in the previous round on 34 minutes.
Michael Carrick's quickly taken free-kick found Defoe on the edge of the box, but this time the England striker fired a blistering shot just over the bar.
Forest refused to lie down and Taylor could have got his name on the scoresheet a lot earlier on 42 minutes.
Rogers caused all kinds of problems for the Tottenham defence down the left-hand side before playing a pin-point cross into Taylor whose downward header forced Robinson to collect the ball at the second attempt.
Brown was desperately unlucky not to get his name on the scoresheet on 43 minutes after Reto Ziegler saw his close-range shot blocked inside the box.
The rebound fell kindly to Brown who saw his fierce shot cannon back off the post and away to safety.
Tottenham finally made their Premiership superiority count on the stroke of half-time when they broke the deadlock and a moment Doyle will clearly want to forget.
Defoe's free-kick from the edge of the box appeared to cause no problems for the teenage keeper, but he failed to hold on to the ball and watched in despair as the ball trickled over the line.
But all credit to Megson's side for the way they responded in the early stages of the second half.
On 51 minutes, Commons showed once again that he can compete at the highest level when he outpaced Timothee Atouba and fired a low drive which produced another fine save from Robinson.
And they finally got their just rewards when Taylor pulled his side level on 56 minutes.
Rogers played a high ball over the top of the Tottenham defence which Robinson and Ledley King appeared to leave for each other.
Taylor nipped in to head the ball over Robinson and slide the ball into an empty net.
Tottenham had Robinson to thank once again for keeping them on the game on 67 minutes when Commons cross-shot forced an acrobatic one-handed save from the England keeper diving away to his left.
And his opposite number Doyle showed he was not affected by his howler in the first half when he made a superb save to deny Defoe on 72 minutes.
But it was Robinson who stole all the headlines when he made another world-class save to deny Commons a certain winner just three minutes from time.
Commons found himself clean through on goal right at the death, but his low drive once again produced a stunning save from the Spurs keeper to ensure a replay at the City Ground in nine days time.