League One outfit Port Vale almost caused a major upset after Leon Constantine had fired his side into the lead at White Hart Lane
But Constantine went from hero to villain when he contributed to Spurs' leveller late in the second half which sent the game into extra-time and Tottenham finally showed their class in the additional 30 minutes.
Despite Vale keeper Mark Goodlad producing a string of world-class saves, it was left to Huddlestone and Defoe to ensure they stayed in the hat for the next round.
But it was Vale who dominated the opening exchanges and could have opened the scoring after just eight minutes.
Danny Sonner made space for himself in the Tottenham half before unleashing a 30-yard drive which flew just over the bar.
And two minutes later Akpo Sodje picked out Jeff Smith inside the box, but he fired a close-range shot wide of the post.
Tottenham slowly eased their way into the game and Steed Malbranque began to show why he could become a regular addition to the first team.
The former Fulham midfielder weaved his way down the right on 12 minutes before feeding the ball into Defoe, who saw his shot fall inches past the post.
Defender Lee Young-Pyo was making a rare appearance in the Tottenham side this season, but almost broke the deadlock on 15 minutes when his fizzing shot from the edge of the box saw Vale keeper Goodlad make a fine save diving low to his right.
Tottenham were starting to make their Premiership superiority count and Defoe came even closer on 24 minutes when his clever lob produced a superb one-handed save from Goodland diving away to his left.
The England striker was causing all kinds of problems for the Port Vale defence and saw Goodlad deny him once again on the stroke of half-time.
Defoe forced his way past two defenders before drilling a low shot which saw the Port Vale keeper at his very best once again to tip the ball around the post.
Despite the home's side dominance, Port Vale almost snatched a shock lead on 49 minutes when Constantine's acrobatic scissor kick flew inches past the post.
Defoe must have wondered if it was going to be his night after Goodlad denied him once again on 56 minutes.
And the home side were made to pay for all their missed opportunities when Constantine put Vale into the lead on 64 minutes.
Sodje's ball into the area fell kindly to the former Millwall striker and he struck a close-range shot through the legs of Radek Cerny to send the Vale fans into ecstasy.
But after Goodlad had denied substitute Dimitar Berbatov with another fine save, Tottenham finally got their just rewards when they grabbed an equaliser on 80 minutes.
Tom Huddlestone's free-kick into the box went in off the arm of Constantine and flew into the bottom right-hand corner.
The game went into extra time and Goodlad kept his side in the game yet again on 92 minutes when he made a superb reflex save to deny Berbatov's header.
But he was left stranded on 99 minutes when Berbatov laid the ball back to Huddlestone and he fired an unstoppable 30-yard shot which deflected in off Sonner.
And Defoe sealed victory for Spurs a minute into the second half when he slid home a cross from Phil Ifil to book a place in the last eight of the competition.