Adebayor, who is on a season-long loan from Manchester City, scored twice on Sunday to inspire Tottenham to a battling 3-1 win over Swansea, their first Barclays Premier League victory in six attempts.
Adebayor arrived at White Hart Lane with concerns about his temperament, attitude and ability, but he has defied his critics to score 14 goals and give the Londoners a very good chance of qualifying for next year's Champions League.
The striker is reported to earn around £170,000 a week at the Etihad Stadium, a figure way beyond what the maximum earners take home at Tottenham, but Van der Vaart rates his team-mate as one of the best strikers around and wants him to stay.
"He is one of the best, a top striker," Van der Vaart said.
"He played for Real Madrid, for Arsenal, Manchester City. I was surprised that he came and I hope that he stays.
"He works his socks off, he's unbelievable. He's so positive. We love him here.
"I played with (Ruud) Van Nistelrooy (at Real Madrid) and he was fantastic and with Ade (Adebayor) as well.
"Normally strikers wait for the chance and they score, but he works hard as well and even when he doesn't score, he's still important for the team. He's a big man for us."
Van der Vaart has been one of the main beneficiaries of Adebayor's arrival.
The Dutchman has formed a strong bond with the 6ft 3in striker, who powered home two headers in the final 17 minutes to kill off Sunday's game after Gylfi Sigurdsson had equalised Van der Vaart's opener.
Van der Vaart, himself one of the club's top earners, acknowledges Adebayor's wages could quash any hopes of his strike partner staying beyond the end of the season.
"I think the problem is the wages," Van der Vaart added.
"Yes, I have tried to persuade him to stay.
"Last season I had a good understanding with Peter Crouch, but with him it's even better. He's tall and strong. He's not selfish and his attitude is one of the best."
Spurs looked back to their best on Sunday, with Van der Vaart, Adebayor and Gareth Bale all excelling in a confident display at White Hart Lane.
Harry Redknapp's team had squandered a 10-point advantage over Arsenal in the race for third, but the win over Swansea means the Gunners only lead their rivals on goal difference with seven games remaining.
Arsenal's defeat at QPR on Saturday saw their seven-match winning streak come to an end and Van der Vaart hopes Arsene Wenger's team will buckle in their run-in.
"I hope they (Arsenal) are getting nervous," Van der Vaart said.
"It was an important match for them away at QPR. That result helped us.
"It's not going to be easy (to finish third), but if we play like we did against Swansea we have a good chance."
On paper Tottenham stand a good chance of pipping their north London rivals to third.
Arsenal play Manchester City on Sunday and also have to host Chelsea, while the highest-placed team Spurs face in their run-in is Sunderland, who currently sit in ninth.
Van der Vaart wants to finish in third not just to give Spurs fans bragging rights - they have not finished above Arsenal since 1995 - but also because it will mean the club avoid playing a qualifier to get in to the Champions League.
"It's important for the whole club to finish third because you never know, in qualifying there are also some big teams, some good teams," he added.
Meanwhile, Press Association Sport understands Tottenham have taken 17-year-old left-back Cristian Ramirez on a 10-day trial from Ecuadorian club Independiente del Valle.
The defender represented Ecuador at the Under-17 World Cup last year and will train with Spurs in the hope of sealing a permanent deal.