Yossi Benayoun and Dirk Kuyt gave Liverpool a 2-0 lead at halftime and Lucas Leiva added a third in the 87th.
Liverpool's 22nd victory of the season takes the team to 77 points from 35 games. Defending champion United, which beat Middlesbrough 2-0 Saturday, has 80 points with a game in hand and could match Liverpool's all-time total of 18 league titles.
"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," Liverpool manager Rafa Benitez said.
"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."
Newcastle's latest defeat leaves it in 18th place, three points away from safety with only three games to go. Hull, which is 17th, can move closer to safety by beating Aston Villa on Monday.
"Time is running out but we've still got two very important home games which will decide our fate, no doubt about that," Shearer said. "The game with Middlesbrough, whoever loses that will find it very difficult to come back. But I believe we will get something from our next two home games."
Newcastle manager Alan Shearer dropped his former England striker partner Michael Owen to the bench while Liverpool had Steven Gerrard back in the lineup after a groin injury but missed Fernando Torres, who is sidelined with a hamstring problem.
After Newcastle goalkeeper Steve Harper had twice saved long-range shots from Gerrard, Kuyt missed an easy chance when he headed the ball across face of the goal.
But Liverpool went ahead in the 22nd minute when Kuyt intercepted the ball inside the Newcastle area and crossed for the unmarked Benayoun to turn the ball home with his left knee from five meters (yards). Benayoun appeared to offside.
More woeful defending led to the second goal six minutes later when no one prevented Kuyt from meeting a corner by Gerrard and scoring with a diving header.
Xabi Alonso almost added a third in the 40th minute with a dipping, 25-meter (yard) shot that hit the crossbar.
Newcastle was left with 10 men after Joey Barton was sent off in the 77th minute for a lunge at Alonso and Liverpool added a third when Lucas headed home a free kick by Fabio Aurelio.
Also, Everton moved ahead of Aston Villa and into fifth by beating Sunderland 2-0 and leaving the Black Cats only four points above the relegation zone.
Steven Pienaar gave Everton the lead in the 48th with a close range shot after Phil Neville and Jo had opened up the Sunderland defense. Marouane Fellaini turned home a cross from Pienaar in the 71st.
Third-place Chelsea beat Fulham 3-1 Saturday but is still six points behind United having played a game more. Arsenal guaranteed fourth place, which means a shot at next season's Champions League, by winning at Portsmouth 3-0.
Birmingham City returned to the Premier League when it captured the second promotion spot in the League Championship by winning 2-1 at Reading on Sunday. The loss means that the Royals, who were relegated last season, now have to try and recapture their top-flight status through the playoffs.
Sheffield United, Burnley and Preston are also in the playoffs to decide the third club to be promoted along with Birmingham and Wolves, which finished at the top of the standings and ended the season with a 1-0 victory over Doncaster.
