Mauricio Pochettino's side face Watford on Saturday after staging a dramatic fightback in a 3-1 midweek win at Swansea that kept alive their hopes of overhauling Chelsea's seven point lead.
Tottenham looked set for a defeat that would have killed off their hopes until they produced three goals in the final stages of the game at the Liberty Stadium.
Having fallen short in their efforts to push eventual champions Leicester all the way last season, Pochettino's men are desperate to make amends and Vertonghen insists Tottenham are now capable of sustaining a title challenge.
"We have shown in the last year or two what we are capable of. People always said Tottenham were able to beat the smaller teams but not the big ones," Vertonghen said.
"In the past couple of years, we have been doing both. Teams are now keeping us in mind when they talk about winning the league or finishing in the top four. Before, it was always 'Tottenham will finish fifth or sixth'.
"In the past two seasons, we have proved we belong where we are. We have some massive quality.
"I don't know what is necessary to win the league, maybe a bit of luck, but there is something very special about this group.
"Chelsea are looking very strong. We won’t stop pushing for the title and dreaming about it, but they had a big win over Manchester City and the gap is still seven points.
"They have difficult games coming up, though, so we have to keep winning and, hopefully, they get a bit stressed."
Son Heung-Min was on target in Tottenham's escape act in south Wales and the South Korean forward insists the team will not give up on the title race.
"We're just keeping going. We don't look at other teams, we have to look at our games and our performances," Son said.
"You never know what will happen and that's why we have to fight for three points in every game."
Tottenham goalkeeper Hugo Lloris withdrew from the Swansea game because of illness but is expected to return to face Watford.
Walter Mazzarri's side virtually secured their Premier League future this week with a victory over West Bromwich Albion that moved them to 10th place, nine points clear of danger.
Mazzarri is keen for Watford to see out the season on a high following reports this week suggesting the future is in doubt partly because of his failure to learn English.
The Italian's plans for the trip to White Hart Lane have been hit by a fresh injury to keeper Heurelho Gomes, while defender Miguel Britos is suspended after being sent off and fellow centre-backs Sebastian Prodl and Younes Kaboul are still out.
However, Watford midfielder Abdoulaye Doucoure says his team will face Spurs free from any pressure.
"The pressure is on Tottenham. Now we are mid-table we do not have a chance to be relegated while Tottenham are fighting for the title," he said.
"The pressure is on them, we have nothing to lose and have to play free like against West Brom. If we can do that you can see what we can do."