With Wayne Rooney making a successful comeback from his gashed thigh and Darren Fletcher completing the full 90 minutes on his first start since it was revealed he was suffering from a chronic bowel complaint 10 months ago, it was a satisfactory evening for Sir Alex Ferguson's men.
Papiss Cisse did give the hosts a scare when he followed up his first goal of the season by crashing a late overhead kick against the bar.
Anderson had put Ferguson's side in front just before the break, and United's youthful defence held on to seal a last-16 berth.
Despite recording five successive victories since that disappointing defeat at Everton in their opening game, there still seems to be an obvious deficiency in the red ranks.
A demand for midfield reinforcements has gone unheeded by Sir Alex Ferguson since before Paul Scholes' retirement.
Attempts have been made to lure a creative force to Old Trafford in the form of Samir Nasri and Luka Modric.
Yet, more obviously, it is a physical presence they lack, someone in the Yaya Toure mould.
So, on an evening when Fletcher was named captain, more interest was in Anderson.
Signed as a teenager from Porto in 2007 for a fee it was estimated would eventually reach £20million, the midfielder has flattered to deceive.
Dogged by injury, the Brazilian has rarely put together anything like a consistent series of performances and more than once it has appeared his time at United was over.
Yet, physically at least, he remains the player in the ranks most capable of imposing himself on the opposition in the way Toure does up the road at City.
So, after a typically inconsistent performance, the manner in which Anderson broke the deadlock a minute before the break was another example of what could be.
Picking the ball up 40 yards out, Anderson ran hard towards the Newcastle box, neatly manoeuvring himself into a shooting position from where his well-struck effort flew in off the inside of Rob Elliot's right-hand post.
It gave the home side a half-time advantage they just about deserved.
Although their defence boasted just two appearances between them, for the most past they kept Newcastle at bay.
Dan Gosling wasted a decent chance and returning skipper Fabricio Coloccini had a header deflected wide, but with debutant Marnick Vermijl and England Under-19 international Michael Keane both impressing, United could go forward with confidence.
Cleverley should have scored after 34 minutes when he strode onto Javier Hernandez's lay-off.
But with just Elliot to beat, the England international sent the ball flying wide, much to his own disbelief.
Vermijl crossed dangerously for Hernandez straight after the restart, only for the Mexican to send his near-post header narrowly wide.
Newcastle carried a threat though. Haris Vuckic was not far away when he got the better of Keane inside the box and took aim for the far post.
After his earlier woeful effort, Cleverley was eager to make amends.
Collecting Welbeck's pass, the England man only had one thought on his mind.
And virtually as soon as the shot left his foot, he set off in celebration at such a landmark moment as his first goal for United nestled in the Newcastle net.
Within a minute of his introduction though, last season's scoring sensation Cisse scored his first of this term, a close-range header from a cross delivered from the left by fellow substitute Shane Ferguson to breathe fresh life into the tie.
In response, luckless Hernandez crashed a shot against the bar.
Rooney's exit 14 minutes from time led to Nick Powell's introduction, confirmation of a Ferguson masterplan that went way beyond the actual result.
With the clock ticking down, Cisse's overhead kick came crashing back off the crossbar.
It was as close as Newcastle came to an equaliser, although the late exit of Alexander Buttner threatened to give Ferguson another defensive headache.