The Hammers downed Chelsea at the London Stadium last weekend and then held Arsenal to a 0-0 draw in midweek.
Noble is delighted with the four-point haul and now wants West Ham to claim all three points at Stoke which would see his side leapfrog their opponents in the Premier League table.
"We needed results and the last two we got against two of the best teams in the league," he told the club's official website. "It's been fantastic, but now we have to go and beat Stoke away.
"They're in a similar position to us and we need to get three points there, and it would top off a fantastic week."
The Hammers remain in the bottom three despite their upturn in form although Noble is confident they can pull clear of danger if they can replicate the kinds of performances they put in against Chelsea and Arsenal.
He added: "It is going to be a battle, but I think anywhere from ninth or 10th downwards, if you get a couple of wins, you're back up with them. This league, at the minute, is so tight, but we're looking a lot stronger.
"If we can keep that form going into these couple of games I'm sure we will be fine."