Kaboul has been used sparingly this season, having only recently returned from a year on the sidelines due to a long-term knee injury.
However, he played for over two hours in midweek as Spurs beat Hull City 8-7 on penalties following a 2-2 draw after extra time.
"Kaboul was extraordinary on Wednesday," Villas-Boas told reporters. "We planned to take him off in the 60th minute. He was giving me signs he had to come off in the 63rd minute, but that was when Nacer Chadli was injured, and he gave the thumbs up to continue.
"It was good that he played 120 minutes. I think we've finally buried his recurrent injuries. That's a great credit to the player and our medical department.
"There is a possibility he will make the team selection to start at Everton."
Kaboul made just one first-team appearance last season.