The midfielder's double from the spot was enough to ensure the pre-season promotion favourites leapfrogged Southampton, who do not play until Monday.
But despite their lofty position, the Hammers rarely hit the heights against a struggling Nottingham Forest side.
In fact, Sam Allardyce's men could, and probably should, have been two or three goals down before they benefited from some generous refereeing, allowing Noble to make it three successful spot-kicks in his last two outings.
Referee Tony Bates twice took centre stage, penalising Guy Moussi and Chris Gunter for handball in each half to gift the hosts victory, despite a last-gasp consolation from Lewis McGugan.
Forest had by far the better chances in the first half, with Marcus Tudgay twice blazing over and McGugan also wayward in front of goal.
Their best opportunity came 15 minutes before the break when former West Ham striker Marlon Harewood and McGugan combined well to tee up Paul Anderson with the goal gaping.
But Hammers defender Julien Faubert just did enough to put Anderson off the shot and Rob Green was able to collect his weak effort.
The home side, by contrast, had created only half-chances, with skipper Kevin Nolan inches away from getting a touch on a dangerous cross from George McCartney and Jack Collison shooting too close to Lee Camp.
But they were handed the lead in first-half stoppage time when referee Bates awarded a penalty after harshly adjudging Moussi had blocked Sam Baldock's cross with his hand.
Noble, whose penalty was all that separated the sides when West Ham beat Portsmouth last week, repeated the trick despite Camp getting a hand to his shot.
The West Ham goal continued to lead a charmed life after the break, with Green making a fine save to deny Chris Gunter.
And from the resulting corner, McGugan's cross deceived everyone in the goalmouth and cannoned off the far post before it was hacked off the line by Noble.
At the other end Collison should have doubled the hosts' lead after a mazy run into the area but his shot was deflected over the top, and Camp pulled off a fine diving save to deny Henri Lansbury.
But the second goal did arrive in the 63rd minute when Bates pointed to the spot again, Gunter this time the guilty party, and Noble did the honours once more.
McGugan pulled one back deep into stoppage time but there was barely time to restart and the Hammers celebrated hitting top spot.