Premier League new-boys Wolves more than held their own against the Hammers apart from where it mattered most - in front of goal.
Wolves could not find a way past in-form Hammers goalkeeper Robert Green and Noble and Upson showed them how cruel life can be in the top-flight with a goal in each half.
Noble fired United ahead with a smart finish in the 22nd minute before Upson made the game safe after 69 minutes.
Wolves had more than enough chances of their own but Green pulled off a series of save to deny Nenad Milijas at the start of the second half and that ultimately proved to be their undoing.
Andy Keogh should have given Wolves the perfect start after just 13 minutes but he missed the ball just six yards from goal and Noble punished them for that let-off.
There initially appeared little danger when former Wolves loanee Carlton Cole rolled the ball across the face of the area.
But Noble was left in acres of space by the Wolves defence and calmly curled home his shot from 20 yards beyond stranded goalkeeper Wayne Hennessey.
Wolves were ultimately fortunate to get to the break just trailing by one goal as they did well to survive a frantic 60 seconds of pressure on the half hour.
Hennessey beat out a shot from Cole and then Jody Craddock cleared the follow up drive from Kieron Dyer off the line.
From the resulting corner, Cole's header was tipped over the bar by Hennessey, who was again called into action seconds later to block a cheeky back heel from Dyer.
Wolves enjoyed their best spell of the game after a half-time pep talk from manager Mick McCarthy but they found Green an immovable object.
Three times in the space of a minute he frustrated Milijas before Wolves had another major escape when Kevin Foley cleared off the line from Jack Collison after Craddock had missed his clearance.
Green then denied Sylvan Ebanks-Blake before the Hammers sealed their success when Noble floated over a corner that the unmarked Upson headed home from eight yards.
Wolves' frustration was then perfectly summed up in the final minute when Green again pushed out a hand to beat away Richard Stearman's header.