The victory came at a heavy cost, however, with defender Michael Dawson suffering what manager Harry Redknapp feared was a season-ending injury.
Defoe fired in the equaliser in the 26th minute after feisty Stevenage took a shock lead at White Hart Lane through a fourth-minute Joel Byrom penalty.
Emmanuel Adebayor made it 2-1 in the 55th from the penalty spot before Defoe made the fifth-round replay safe with a 75th-minute shot from the edge of the box.
Tottenham, the eight-times cup winners and currently third in the Premier League, will host fellow Premier League Bolton Wanderers in the last eight.
"It was tough. I didn't come here tonight expecting it to be easy," Redknapp told reporters. "They are big, strong and great on set plays. Every corner is a problem."
Dawson was carried off on a stretcher after just nine minutes and winger Aaron Lennon was also injured.
"It looked like his ankle. Looking at his injury tonight it would be a miracle [if he played again this season]," Redknapp said of Dawson.
"He's a great guy and a fantastic professional and a big loss to us. We want Michael in our team that's for sure."
Lennon went off just before half-time with a recurrence of a hamstring injury that has plagued him all season and could also miss Saturday's trip to Everton.
Asked about his priorities for the season, Redknapp said; "We want Champions League football and we want to win the FA Cup. Both are important.
"It's good to see Jermain back scoring. He's a good finisher and a good player when he's in that type of form."
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