The duo produced two impressive goals to put the Red Devils ahead and Sir Alex Ferguson's men held on despite a Papiss Cisse-led fightback in the second half at Old TraffordManchester United progressed to the League Cup's fourth round with a 2-1 victory over Newcastle in a hard-fought open match that saw both sides hit the woodwork.
The Red Devils were on top for the majority of the first half, and should have took advantage when Anderson and Tom Cleverley both had brilliant chances, but did eventually take the lead courtesy of a superb strike from the Brazilian.
Alan Pardew's men tried to work their way back into the clash after the break, having a couple of decent chances, but Cleverley fired home to extent the hosts' lead. Papiss Cisse pulled a goal back with a half hour left, but it wasn't enough to stop his side crashing out.
Sir Alex Ferguson named a strong lineup for the tie at Old Trafford, with Wayne Rooney returning from injury as well as Darren Fletcher, Danny Welbeck, Chicharito and David de Gea all starting.
The visitors made a number of changes from his first-team side that beat Norwich in the Premier League, with a few unfamiliar faces among the starters, though Fabricio Coloccini and Cheick Tiote both returned.
After the home side dominated the opening ten minutes, the Magpies had the first real chance of the game when Dan Gosling volleyed over from six-yards out. The midfielder had time and space to pick his spot but sliced the effort well wide after Shola Ameobi's nod down.
Moments later the hosts appealed for a penalty after Rooney was tripped in the area, but nothing was given. Then they came forward again as Anderson broke from midfield, wasting a great chance by shooting wide.
Ferguson's men continued to play the better football, though Newcastle looked dangerous on the counter and had a number of decent openings but failed to create a final chance. Welbeck, however, managed to muster a shooting opportunity as he fired a strike towards the corner which Elliot parried away.
Ten minutes before halftime Cleverley made an complete mess of a brilliant opening, from which he should have put his side 1-0 up. After some brilliant play from Chicharito on the right-hand-side, and some neat touches from Rooney and Welbeck, the England midfielder was left with a one-on-one with Elliott from no more than three yards out, but somehow shot wide.
United did take the lead just before the break, though, as Brazilian midfielder Anderson held off a challenge from his man before smashing the ball into the top corner with his left boot from outside the box, via a touch from the post, after picking it up from Fletcher.
Two minutes after halftime the former Benfica man had a good chance to bag a second. He started the move with a great ball to Welbeck on the left flank. He then returned the favor, but Anderson lashed his first-time strike over the bar.
As Ferguson's men looked to push home their slight dominance, it was the visiting team that had the next good opening as Haris Vuckic smartly worked his way past Michael Keane in the box before curling a strike just past the post.
They were left to rue that miss just under five minutes later. Welbeck picked up the ball on the edge of the box and shifted it central to Cleverley, who riffled a strike into the corner just out of Elliot's reach.
The two-goal cushion didn't last long however, as Cisse came off the bench and made an instant impact by rising highest to head home from Shane Ferguson's cross to pull one back.
With a comeback looking on, as Newcastle pushed forward, Chicharito almost gave the home side the perfect response, hitting the bar from a narrow angle with a powerful effort, before Anderson thundered a deflected shot not far over the bar.
The Magpies continued to look for an equalizer, throwing numerous balls into the United box for Ameobi and Cisse to attack. The latter also crashed the bar with a fantastic overhead kick after he chested the ball up for himself just inside the box.
Ferguson's men, however, held off other half-chances from the visitors late on, securing the win and march on to the next round.