But Defoe's clinical finish in the 61st minute put his side on level terms before Tom Huddlestone was handed the chance to win it for Spurs when Sam Ricketts handled in the box.
Huddlestone failed from the spot, though, and the sides will now meet in a replay at White Hart Lane.
However Bolton, who created four decent openings in the opening quarter of an hour, should have had a comfortable cushion before allowing Spurs back into the game.
Johan Elmander's ninth-minute shot was deflected over by Vedran Corluka after Chung-Yong Lee's cross came back off Matt Taylor, Zat Knight volleyed straight at goalkeeper Heurelho Gomes and Elmander's threatening run into the left of the area was halted only by Huddlestone's well-timed tackle.
However, the Swede was more culpable when he was sent clear by Ricardo Gardner's 15th-minute through-ball as his first touch took him wide and his second saw him blaze wildly over with his left foot.
Taylor was next to threaten with a low curling 30-yard free-kick which Gomes did well to turn around the post.
Bolton's pressure eventually told in the 34th minute with a flowing move for which Owen Coyle's sides have earned a reputation.
Gardner's threaded pass picked out Elmander's diagonal run 10 yards outside the penalty area and he exchanged passes with Lee before crossing from the byline to Davies who took one touch and stabbed home.
Defoe's sole contribution of the first half was to get booked, along with Taylor, for his part in an argument with the Bolton midfielder late on.
Davies almost scored his second two minutes after the break when Lee's cross was laid off by Elmander and the Wanderers captain's shot
was deflected just wide of the post by Michael Dawson with Gomes completely wrong-footed.
The one-way traffic continued with Elmander firing into the side-netting after combining with Fabrice Muamba and Davies to find space on the right of the penalty area.
Muamba should have done better in the 54th minute when a quick counter-attack saw Paul Robinson dispossess Peter Crouch in the Wanderers penalty area and release Davies who in turn sent Elmander racing down the left but when the cross came in the England Under-21 international screwed his shot wide.
Tottenham had two chances to equalise within the space of the next 120 seconds but were denied twice by the woodwork.
Firstly Crouch beat Jaaskelainen to head against the crossbar and then Wilson Palacios' driving run and cross saw Robinson deflect the ball up and on to the top of the frame of the goal.
Spurs eventually made the breakthrough in the 61st minute when Gareth Bale cut into the area and picked out Defoe on the penalty spot who took a touch before firing high into the net.
Six minutes later substitute Niko Kranjcar, on for the ineffective Modric, lashed in a 25-yard shot which Jaaskelainen had to tip around the post at full stretch.
With 19 minutes remaining Spurs were handed the chance to score a second when Crouch's attempt to lift the ball over Ricketts saw it hit the defender's arm.
However, Huddlestone's effort from the spot was poor and Jaaskelainen saved to his right.
The goalkeeper was called into action again moments later to turn Defoe's shot around the post.
After such inactivity earlier in the game it was Spurs who finished the stronger but Bolton held out to earn a trip to White Hart Lane.