The Spurs manager says that Arsene Wenger's side can draw on their history of finishing seasons strongly, but insists that his team will not "look at ghosts in the past"
Spurs have won just once in their last six matches, and a similar late run of poor form last season saw the club finish a point behind Arsenal in fourth and miss out on the competition in place of tournament-winners Chelsea.
The Gunners, meanwhile, have won their last three on the bounce since slipping to defeat against their rivals at White Hart Lane, with Villas-Boas noting that Arsene Wenger and his side can draw on belief from finishing seasons well in the past.
"Arsenal's game in hand is against Everton, so something is going to happen," Villas-Boas told reporters.
"We don't look at ghosts in the past. It definitely looks like it's going to go down to the wire. The reality is that Arsenal feel their belief because they finish seasons very strongly and that belief helps them."
Spurs have reached the quarter-finals of the Europa League but a run of just one win in six matches has prompted suggestions that the team are suffering from fatigue, having lost key attackers Gareth Bale, Aaron Lennon and Jermain Defoe to injury in recent weeks.
The manager did not accept this, though, and insisted Sunday's 2-2 draw against sixth-place Everton was a good result after Gylfi Sigurdsson's late equaliser.
"It's nothing to do with our tiredness," he added. "It was important for us to salvage a point because, against teams who fight for the same objectives, the only thing you cannot do is lose.
"It was a good performance by the team, individually and collectively, although not the result that we wanted. It means everybody is tied together for the spots."
Chelsea's FA Cup semi-final this weekend postponed their match against Tottenham, leaving Thursday's Europa League quarter-final second leg as Spurs' only game this week.
Villas-Boas was pleased, adding: "The break allows us to focus completely on the Basel game, which is very important for the football club – it could be a blessing."