Arsene Wenger has only lost once to Spurs in his career and has not tasted defeat to them in eight years, a record that looked threatened when Robbie Keane stepped up to take a spot-kick in the 72nd minute.
Manuel Almunia dived the right way to deny Keane then Bendtner took centre stage four minutes later when he headed in Cesc Fabregas' corner just seconds after coming on for Emmanuel Eboue.
It was the first touch of his career against Spurs.
"You can call that an inspired substitution if you want - it was a welcome goal," said Wenger.
Victory extended Arsenal's lead at the top of the table to four points, even though Wenger admits his side are not playing at full tilt yet.
"We weren't sharp in the first half and we needed to raise our game," said the Frenchman. "When we went ahead we looked like we were in control but we let them back into it.
"Overall, we are conscious that we were not at our best, only in patches. They missed a sitter and Almunia's penalty save was the turning point in the game."
Wenger added: "We can keep getting results. We played a top level game last week against Chelsea and we maybe relaxed a bit after that.
"But we still have 43 points with 20 games to go so we are in a very strong position. You can argue with the points we got today but all the rest, we have got what we deserved.
"Maybe I am a very optimistic man but I always have great belief in my team."