Spurs were far from the free-flowing football we've seen from them in recent weeks as Sean Dyche's notoriously tough Burnley shut down any space in the box.
And the Clarets came the closest to breaking the deadlock when James Tarkowski's header was cleared off the line by Harry Kane.
The goal was Son's eighth for the season, while Kane now has eight assists.
Unlike against West Ham last weekend, Jose Mourinho's side were able to hold onto all three points.
They now move into fifth on the table, only two points from first-placed Everton.
Meanwhile, Burnley are yet to register a win this season and will feel hard done by after the loss to Spurs.