The in-form defender – outstanding again in the third round tie, this time at left-back – struck in the 37th minute at Brunton Park.
Gylfi Sigurdsson curled in a free-kick from the right and Jan was there to head home from close range.
It was an important opening goal after Carlisle had worked tirelessly to upset our rhythm in the first half.
Andros Townsend struck a beauty to make it 2-0 in the 53rd minute as we dominated the second half and Gylfi also bagged his first goal for us to complete a impressive night’s work in the final minute.
“It wasn’t the most beautiful goal but I’m very happy I scored my first goal for Spurs,” said Jan. “I’m very excited about it.
“We needed a goal in the first half and in the second half we played a lot better. We had a few good periods in the game and in the end, it was a good win.
“Carlisle made it difficult. It was their game of the year but we did well, we had a long journey and we showed the right attitude and motivation. I think we can be proud of ourselves.”