Spurs moved ahead of West Ham and Manchester United into fifth spot with the win, sitting on 51 points from 29 games, behind fourth-placed Arsenal on 54 points from 28 games.
Son Heung-Min netted a double, with both goals assisted by Harry Kane, who has hit top form recently as Tottenham have begun building some momentum.
Spurs have won four of their past five league games, as well as five of their past seven including a 3-2 win at Manchester City to offer reason for hope.
“We have this ambition, the ambition is to target fourth place. Before my arrival this seemed difficult to reach, but now after five months, this is starting to work,” Conte told reporters.
“We want to stay in this race until the end. It’s very difficult, but we are improving in a way that I like. This team is growing in the mentality, they are learning to control the game and this is very important.
“There are four teams that in my opinion in England are better than the others - I am talking about Manchester City, Manchester United, Chelsea and Liverpool.
“But if one of these four teams fail in the season and miss to stay in one of the four places, I think that now at this moment, Arsenal, Tottenham and West Ham need to be ready to try to stay until the end.”
Hammers boss David Moyes praised Kane, who has netted seven times and provided three assists in their past seven games.
He said: “I thought Harry Kane was exceptional with the way he played and we found it difficult trying to deal with him.”
Elsewhere, midtable Leicester City claimed a 2-1 home win over Brentford with first-half goals from Timothy Castagne and James Maddison.