The striker had his opening goal cancelled out by Robert Beric in the first half before netting twice after the break to clinch the victory.
Spurs went on the attack from the first whistle as Gareth Bale tormented the Maribor defence from the left side.
Their pressure paid off in the 22nd minute when Defoe guided the ball into the net from the Welshman's cross.
Bale had a chance to double his side's advantage midway through the half, but his tame effort was easily gathered by Jasmin Handanovic.
However, Maribor grabbed an equaliser against the run of play four minutes before the break as Beric charged down Kyle Naughton's backpass to goalkeeper Hugo Lloris before converting.
It took Spurs only four minutes after the restart to get themselves back in front and it was Defoe again who found space in the box before firing left-footed past Handanovic.
Emmanuel Adebayor nearly put the home side out of sight on the hour, but he could only volley wide from Bale's scooped through ball.
The win was sealed with 13 minutes left on the clock as Defoe completed his hat-trick by tapping in from another Bale cross.