But despite that victory Delap refuses to believe Stoke are safe.
"I wouldn't like to say yes or no, but we're on course to better last season's tally and that's what we've set out to do," Delap told BBC Radio Stoke.
Tony Pulis' team finished 12th in their debut season in the Premier League with 45 points.
The victory at Upton Park, thanks to a superb individual strike by Ricardo Fuller, briefly took the Potters into the top half of the table, before Blackburn overtook them on Sunday with a win at Burnley.
Stoke face Hull, another team battling against the drop, at the Britannia Stadium on Saturday.
"We've got to concentrate fully on Hull," said Delap. "It's another game at home that we need to go out and win.
"If we get the win we'll be on 42 points and that will stand us in good stead to better what we did last year."
Source: BBC Sport
Source: BBC Sport