Maurico Pochettino’s men, in third place, have won three of their past four league games and their tally of 70 points puts them three ahead of fourth-placed Chelsea and four clear of Arsenal, in fifth spot.
Manchester United are a further two points adrift.
Christian Eriksen’s late winner against Brighton in midweek was the seventh time they have found a winner in the 80th minute or later this season, showing an impressive never-say-die spirit.
Spurs, who have three league games left to play, lost four out of five Premier League matches before they stopped the rot earlier this month against Crystal Palace in the first game at their new stadium.
“We keep going until the last minute,” said Eriksen. “We had chances and that was the case in the other games as well, games where we should have scored before instead of making it so exciting and nerve-wracking. In the end it’s about taking the chances you get.”
“We needed a result, so did they, and it was patience, building and trying to create something out of nothing. In the end it was a big win,” he added.
Spurs, who host Ajax in the first leg of their Champions League semi-final on Tuesday, travel to Bournemouth on May 4 and then finish their Premier League campaign at home against Everton the following week.
“Before the season started we would have signed up for being in the semi-finals of the Champions League and being where we are (in the Premier League),” said Eriksen.
“Of course we would love to have gone even further in the Premier League as well but at the end you need to win the games you can, we’ve done that in the Champions League and we also need to do that in the Premier League to secure our place in the Champions League again next season.”
– Stadium boost –
The victory against struggling Brighton was Tottenham’s fourth win out of four in their sparkling new stadium. They have scored eight goals at their new home without reply.
Mid-table West Ham, by contrast, have not won any of their past eight league matches on the road, failing to score in six of those.
Spurs, seeking to qualify for the Champions League for the fourth season in a row, are without injured talisman Harry Kane and Pochettino will be cautious with the Champions League semi-final looming.
One player almost certain to feature is Son Heung-min, who is suspended for the European tie and says he is feeling fresh as the season nears its climax.
“If I say I’m tired, maybe other players start thinking the same as me, so if I’m tired I’ll never say I’m tired,” said the South Korean. “I try to keep positive to the other players.
“There’s not many games left. I feel good, I feel all right and the most important games are coming up. There’s big challenges ahead so I’m looking forward to playing with fresh legs.”