The Magpies fell behind on the stroke of half-time at the Amex Stadium following Leandro Trossard's curling strike before Danny Welbeck doubled Albion's advantage six minutes after the restart.
Neal Maupay grabbed Brighton's third with a close-range volley to condemn United to a consecutive 3-0 defeat against the Seagulls after losing by the same scoreline in September's reverse fixture at St. James' Park.
The visitors were fortunate not to fall behind inside 120 seconds as Ben White released Neal Maupay on the right wing before the Frenchman's teasing cross founds its way to Jakub Moder at the back stick but the Pole's half-volley was fired wide of the target.
United goalkeeper Martin Dúbravka prevented Moder from breaking the deadlock a minute later as the midfielder got onto the end of Danny Welbeck's cross from the left flank but his first-time effort was held by the Slovakian shot-stopper.
Yves Bissouma, who received a red card against the Magpies in September, was teed up by Trossard on the edge of the box but the Malian midfielder's low effort flew straight into the arms of Dúbravka.
Newcastle's sole attacking opportunity of the first-half fell to Isaac Hayden as the central midfielder headed wide at the far post following Jonjo Shelvey's swinging cross.
Ciaran Clark produced a key block to deny Maupay from scoring moments later after the Frenchman met Trossard's low cross, after the winger raced onto Pascal Groß's neat through ball, but the striker's close-range effort was importantly blocked by the Irish centre-back before the ball was eventually cleared from danger.
As Hayden was stretchered off following an accidental collision with Bissouma, the Magpies were dealt another significant blow as Trossard broke the deadlock in the final minutes of the first-half.
After controlling Joël Veltman's lofted pass on the edge of the box, the Belgian jinked inside before his curling effort on the edge of the penalty area flew beyond Dúbravka into the far corner.
Newcastle almost got back on level terms four minutes after the restart as Ryan Fraser was denied a first Premier League goal for the Magpies after striking the woodwork.
After Almirón picked out the Scotland international on the corner of the box, the winger's first-time effort curled past the diving Robert Sánchez before clipping the outside of the post.
In the 51st minute, Brighton extended their lead as Welbeck was allowed time and space to cut inside from the left wing before the former England international bent a fierce effort into the bottom right-hand corner.
In the 68th minute, Newcastle trailed by three goals as Maupay, who recorded a brace in the Seagulls' 3-0 win on Tyneside, steered home Groß's cross from the right flank to end a run of nine Premier League games without a goal.
Graham Potter's side, who had recorded one win in 14 Premier League home matches this term before facing Newcastle, continued their push for a fourth goal as Welbeck beat the offside trap before racing through on goal but the former Sunderland forward's effort was pushed around the far post by Dúbravka.
The Magpies were unable to register a late consolation, with just one shot on target during the 90 minutes, as Brighton moved four points clear of Newcastle, who sit two points above the relegation zone.
Newcastle United: Martin Dúbravka, Javier Manquillo, Jamaal Lascelles (c), Ciaran Clark, Paul Dummett, Isaac Hayden (Jeff Hendrick 45), Jonjo Shelvey, Joe Willock (Jacob Murphy 62), Ryan Fraser, Miguel Almirón (Sean Longstaff 76), Joelinton.
Subs not used: Karl Darlow, Federico Fernández, Jamal Lewis, Matt Ritchie, Dwight Gayle, Andy Carroll.