United had not won a game since 28th October and Alan Pardew's men had lost their last four Premier League matches.
But the result was not in doubt from the 13th minute when Maynor Figueroa was sent off for a debatable shove in the box and Demba Ba slotted home the penalty.
Ba added a second and, after half-time, Gael Bigirimana, 19, scored a sensational third, his first professional goal.
Dutchman Krul admitted Newcastle's injury-hit team were desperate for a win - any kind of win.
"It's a massive win for us," he told Sky Sports. "Tonight, we knew we needed three points. The pressure was on us."
He admitted Newcastle may have been lucky with Figueroa's red card but said: "I don't think we've had many breaks this season. We've lost a lot of players to injuries and luck has not been on our side.
"But I think we put a lot of effort in and I think we can be proud and take a lot of confidence out of that.
"It's been hard. Injuries and losing games - it's a new experience for us especially as we had a great season last season. We're coping well - we need to stick together and I think tonight we showed what a quality team we are. We needed this."
Bigirimana, 19, said: "Me and Papiss Cisse were planning to dance if we scored but it was my first goal ever as a professional and I just gave thanks to God.
"It's hard to come to a new club as a young player but you've got to step up - the manager bought us so he trusts us."