Spurs were always dominant in the game and opened the scoring mid-way through the first half, but were forced to work hard for the win after a defensive mix-up gave Maribor an unlikely foothold in the game with a 1-1 half-time scoreline.
In the second half, however, the visitors tired and Defoe took full advantage by completing his hat trick, and overtaking Teddy Sheringham in the Spurs all-time goalscorers list.
But he was more focused on what the win would do for the team.
He told ITV: "We needed to win to bounce back from the weekend [defeat to Wigan].
"We pressed high from the minute go. The tempo was good, the movement was good, we kept the ball better and we're all delighted."
The striker was honoured, however, to have overtaken Sheringham.
"Its special to go past Teddy," he added.
"He was a great player for club and country. I watched him when I was growing up so it's great for me personally."
Gareth Bale had another inspirational display from wide positions. And he insisted the players were determined to win the competition.
He said: "Everyone wants to be playing in the Champions League, but this is the next best thing, we're taking it seriously and hopefully we can do well."