Spurs are now level on points with Manchester United and just three behind leaders Manchester City after another convincing performance as Everton were beaten 2-0 at White Hart Lane.
It is a remarkable turnaround in fortunes from August, when Harry Redknapp's men lost their opening two games, against United and City, after the original fixture against Everton had been postponed because of the London riots.
Spurs could wipe out City's lead if they beat Wolves at home on Saturday ahead of the Blues' trip to Wigan on Monday night, and Van der Vaart sees no reason why they cannot last the distance.
"Everybody knows Spurs have a great team and if we can keep playing like this, then we're also favourites to win the title," Van der Vaart told the London Evening Standard.
"We know we are good and apart from the first two games, we have won almost every week.
"When we played Man City in August, they were too good but in the last few games they have not been as consistent and they lost on Wednesday night too (against Liverpool in the Carling Cup semi-final first leg).
"Maybe it's a little bit in their heads. They have invested so much money, so everyone expects they're going to win it but we're still there. Do we believe we can do it? Absolutely.
"The game against City is massive and we are really looking forward to it, but first we must beat Wolves.
"We are much better now than we were at the start of the season, so I am really looking forward to the games that are coming up.
"City have so many good players that even when they're not playing well, they can decide a game, whereas we're more of a team. It's going to be very interesting.
"We played well there last season but lost 1-0, so we will go there with confidence and there is no reason why we can't win.
"After the game at City, we will know where we stand."
Tottenham had started nervously against Everton, before Aaron Lennon cut in from the right after getting on the end of Benoit Assou-Ekotto's brilliant cross-field pass and slotted past Tim Howard to open the scoring on 35 minutes.
Assou Ekotto then added a second just after the hour when he blasted home a 30-yard effort, which took a slight deflection off Tim Cahill.
The full-back may well have cracked in a potential contender for goal of the season, but it was youngster Jake Livermore who again caught the eye with an all-action display in central midfield.
Spurs boss Redknapp believes the 22-year-old academy product has a bright future.
"Jake was fantastic, absolutely superb and I was delighted for him," Redknapp said.
"You couldn't get a better lad than Jake. He's a fantastic boy with a great attitude and he's a really good player.
"If you had a club full of people like that you'd have a great football club.
"When I first came to the club people said he wouldn't make it at Tottenham - well Jake is good enough to play for anyone."