Goals came from Yossi Benayoun and Dirk Kuyt in the first-half and substitute Lucas with a late header were more than enough against the Magpies defensive frailties.
Toon boss Alan Shearer will hit Joey Barton with a club fine after the midfielder's season was ended by a red card following a two-footed lunge at Alonso that saw the Spaniard carried off with a leg injury.
Shearer said of Barton: "He deserved to be sent off, he has let himself and the club down.
"He was not unlucky, the referee was spot-on. There was no need for him to do that in such a position."
And Shearer pulled no punches with his assessment of Newcastle's performance.
He said: "We were lucky to keep it down to three, how many times did they hit the bar?
"I was disappointed with the manner of the goals. The first was offside and the second and third were from set-pieces. If you give players things to do at set-pieces and they do not pick up their man, it is very disappointing."
Shearer was goaded by the Kop with "You should have stayed on the telly" chants, and the former England just smiled.
He said: "I wondered if I should have laughed or cried, so I decided to laugh.
"But our fate was not going to be decided here. This is a very difficult place to get anything. Our fate will be decided by our two home games with the next one against Middlesbrough probably the biggest game this club has had for a very long time."
"There were a lot of positives from that victory. We could have scored more and we are closer again at the top and still pushing.
"Manchester United are a good team with good players, and they will need to make two big mistakes to let us in. But I still believe they can be caught and they will make mistakes.
"All we can do is to continue to win our matches and see how they handle pressure. We must win all our games to see how that affects them at the top."