It was a cagey affair to begin with at the London Stadium with some half chances before Adrián brilliantly denied Harry Kane, and a potentially controversial handball from Spurs skipper Hugo Lloris was waved away, inside the opening half-an-hour.
Spurs started the second-half well as they looked to make the much needed breakthrough with Christian Eriksen and Son Heung-min coming close, but it was Lanzini’s effort that proved the difference.
Jonathan Calleri had a great opportunity to add a second, but they did enough to not only mathematically secure their Premier League status but deal their bitter rivals a major blow in the title race.
Chelsea just need to win their next two games - Middlesbrough at home on Monday and West Bromwich Albion away next Friday - to secure the title before Spurs even play another league game.
Took a while to get into first gear
A lot was on the shoulders of this bitter London derby in terms of the title race, with Spurs handed a great opportunity to close the gap on leaders Chelsea - who aren’t in action until Monday night.
The atmosphere was scintillating early on inside the London Stadium, a rarity throughout what has been a majorly miserable season. The game started slow but the visitors were dealt an excellent chance in the 21st minute.
It was the first real break that Mauricio Pochettino’s side had managed as Dele Alli played it through to Kane and he hit a stinging effort down the throat of Adrián which the 'keeper could only palm away.
The rebound fell to the feet of Alli but his effort was blocked by José Fonte and it came back for Kane for a third bite of the cherry but Adrián did excellently, his save with his leg taking the shot over the crossbar.
Spurs are renowned for their defensive record being the best in the current campaign, but their defence was unusually open before the half-hour mark. Mark Noble sprayed the ball over to Lanzini who was left in acres of space and he looked to take it around Lloris who came flying off his line.
The Frenchman flattened the Argentine but the controversy came as it looked like he may have handled it outside the area, referee Anthony Taylor waving away the appeals. And rightly so, as a second viewing showed it came off Lloris’ knee.
Looking to turn the screw
The visitors only had 45 minutes to try and get a goal to keep their slim title hopes alive and Eriksen and Son had two chances in quick succession to try and give them that crucial breakthrough.
The first arrived just before the hour mark as Kyle Walker picked out the South Korean on the right. Son pulled it back for Eriksen but the Dane’s effort was weak as it rolled into the arms of Adrián.
Son came close moments later. Walker did well with his run to open up the chance for the winger, but his low effort was nothing that Adrián couldn't handle as he pushed it wide.
Taking an unexpected lead
There had been little to sing and dance about during West Ham’s opening campaign at the London Stadium, but they were on the path for one of their best league victories thus far when Lanzini gave them an unexpected lead.
The Argentine started the move as he gave the ball to Aaron Cresswell to put it into the box. The ball was kept alive as André Ayew’s effort was blocked but it fell kindly for Lanzini to turn it home from close range.
Spurs looked rattled and Slaven Bilić was left scratching his head how his side didn’t kill the game off with Calleri’s excellent opportunity.
Toby Alderweireld has been one of the best players in the league this season but was made to look a clown as he dispossessed by Calleri. The Argentine turned well to leave him one-on-one with Lloris and it is Frenchman that came out on top.
But the Hammers held on for a huge three points which means the title is almost inevitably headed back to Stamford Bridge.