Christian Eriksen’s late winner saw Mauricio Pochettino’s side re-close the gap on leaders Chelsea to four points with five games to go.
Spurs have now won eight on the trot – and need to continue their winning streak in the North London derby on Sunday.
A home win at White Hart Lane would see Tottenham guaranteed to finish higher up the table than their local rivals for the first time in 22 years.
And Alderweireld said: “It is a massive game. We are going to try and win at the Lane. It is going to be a special day and it is up to us to get three points.
“Beating Arsenal to finish above them is extra motivation but you do not need extra motivation on Sunday.”
Tottenham’s title bid collapsed after the Battle of the Bridge last season – and Pochettino had demanded a reaction from his players after last weekend’s FA Cup semi-final defeat to Chelsea.
After a stuttering first half, Spurs responded with an improved display after the break to allow the leaders little room for error. Chelsea travel to Everton on Sunday – the hardest match remaining on their fixture schedule.
“We want to put pressure on them,” added the Belgium defender. “Of course we want to catch them but we want to defend the second spot as well. The only thing we can do is try to win our games.
“Against Palace, we fought as a team and did very well. We played in a very adult way. We did not give them any chances and we know we have the quality and the creativity up front to make the difference.
“It showed we are not going away in the title race. We try to win our games .We know it is going to be difficult but that is all we can do. This was a good response after the FA Cup semi-final.
“We are back in it. We showed character after Saturday and are back on track. That is very important, if you get a setback to respond immediately.”