Without Real Madrid target Gareth Bale, ruled out because of a foot injury, Tottenham manager Andre Villas-Boas handed starts to Paulinho, Nacer Chadli and Soldado, with the latter the most impressive.
The Spain striker, signed from Valencia for a club record £26million, troubled the Palace back four throughout with his movement and he dispatched a second-half penalty to win the match after Dean Moxey handled Aaron Lennon's cross.
Vertonghen passed a late fitness test to start in defence and was relieved to claim a win in the new-look Tottenham side.
"That's what we wanted. We couldn't get a loss here," Vertonghen told Sky Sports 1.
"Of course we want to do better but this was about getting the win for us. Next time we will score more goals."
Vertonghen, a Belgium international, hailed the new signings made by Villas-Boas over the summer but also praised Palace.
"They (new signings) are strong and Roberto scored a goal," Vertonghen said.
"We have a big and strong team. We want to play for the prizes and Champions League qualification. That's why we need a big team.
"They (Palace) play long balls towards (Marouane) Chamakh and (Kevin) Phillips. We knew that would make it tough and that's what we had to try and get two goals."
For Chadli, who made his debut appearance for Spurs following his summer transfer from Dutch side FC Twente, the first game of the season was more about settling into the English game.
He said: "I really enjoyed it. It was a nice game with plenty of chances. It's most important to get three points.
"It is different to Holland but I like the way we play. We play quickly and that's how we create chances."