Scholes put United on course with a long range strike in the 54th minute - amazingly United's first shot on target - before Ruud Van Nistelrooy sealed their win with his 12th goal of the campaign.
England international Scholes, who last week against Charlton scored his first goal for seven months, then grabbed his second after 82 minutes.
Before the intervention of Scholes and Van Nistelrooy, United had been forced to battle hard by Albion.
United struggled to get into gear in the opening 45 minutes, but were a different proposition after the break when they rarely gave Albion a chance to take something from the game.
The defeat leaves former United skipper Robson still searching for his first win since returning to the club to take over as manager earlier this month.
They are now rooted to the bottom of the table having taken only one point from Robson's first three games in charge.
They paid the price for failing to take advantage of the chances that came their way in the first half against United.
Despite seeing Ryan Giggs fire wide in the 7th minute, United made a sluggish start and it was Albion who made all the early running.
Robert Earnshaw proved to be a constant menace to the United defence and the Welsh international was close to firing Albion ahead after with a ninth minute volley that flashed the wrong side of the post.
Earnshaw then turned provider nine minutes later when nodded the ball into the path of Zoltan Gera.
The Hungarian international captain then powered his way to the edge of the United area before seeking his shot saved by United goalkeeper Roy Carroll.
Little had been seen of United as an attacking force following Giggs' early effort and it even took their new talisman Wayne Rooney fully 21 minutes to make an impact.
Rooney capitalised on a mistake by Andy Johnson and then whipped in a shot from 25 yards that was inches away from breaking the deadlock.
Albion then suffered a setback two minutes later when their inspirational central defender Darren Moore was forced off with a knee injury and replaced by Thomas Gaardsoe.
Despite having to reshuffle their defence, Albion still had little trouble keeping United at bay and Earnshaw continued to look the most potent attacking threat.
He tested Carroll with another drive after 26 minutes before United created the best chance of the half only for Rooney to fluff his big chance.
Van Nistelrooy floated over a cross that picked out Rooney on the far post.
The former Everton marksman was only six yards from goal, but he could not get his header on target under pressure from Riccardo Scimeca and the ball flew harmlessly over the bar.
Fortunately for Rooney his blushes were spared by the impressive Scholes.
He had been growing in stature as the game wore on and capped an impressive display with a stunning strike nine minutes after half-time.
While the goal itself was worthy of winning any game, the build-up play was also right out of the top draw.
United's Argentinean international left-back Gabriel Heinze rolled a pass into the feet of Giggs who nonchalantly flicked the ball to Scholes.
He looked up, moved a few paces forward and beat the Albion goalkeeper Russell Hoult with a powerful shot that fizzed into the back of the net.
That really was the beginning of the end for Albion and van Nistelrooy sealed their fate 18 minutes from time.
Once again it was a goal created by Giggs and Heinze. This time, Giggs floated in a free kick, Heinze rose to head the ball back across the face of goal leaving van Nistelrooy the simple chance to nod home from three yards.
United were in cruise mood after that and Scholes gave the scoreline a somewhat flattering look after 82 minutes.
He had the simple task of heading home from close range after being picked out by Rooney.
Man of the Match: Paul Scholes - The former England star showed he is back to his best with an impressive display which was rewarded with a two-goal haul.