The Hammers made a poor start to the campaign, losing their first four games, but their form improved with wins over Everton and Manchester United and a draw against Chelsea before a disappointing defeat at Brighton before the international break.
They're 15th in the table and face another tough test at the London Stadium on Saturday.
Tottenham make the short trip across London and Fabianski believes they are capable of causing an upset.
He told the club's official website: "It's another important one, another big one against a tough opponent, but we are playing at home so hopefully with all the hard work during the week we'll be in good form for Saturday's game.
"I'm looking forward to the atmosphere on Saturday. I've always enjoyed playing against Spurs - it has a nice atmosphere to it so I'm guessing it won't be any different.
"We just have to prepare ourselves well during the week and have a good game on Saturday, and make sure that the fans will be proud and happy after our performance.
"You can see that we have improved, especially playing at home and the recent results here have been very good so hopefully that will continue this Saturday."