The 23-year-old Gakpo, a January recruit from PSV, marked his first appearance in this famous rivalry with a pair of sublime goals, with Nunez and Salah adding to the humbling on Sunday.
Salah became Liverpool's record Premier League scorer and substitute Roberto Firmino also got in on the act, on what was a day of vindication for manager Jurgen Klopp.
Liverpool's German boss sees Gakpo and Nunez as vital to the team's future, and against a ragged United defence they helped make it a day to savour for the hosts, whose win takes them above Newcastle United and into fifth place.
Erik ten Hag's Red Devils, seven days on from winning the League Cup at Wembley, were abject.
They are seven points better off than Liverpool and remain third in the table, but they trail leaders Arsenal by 14 points and have only 13 games remaining. This will also take some getting over.
Liverpool had most of the early possession, but the key chances in the opening half-hour were created by United, with Antony having the first when his low shot towards the left corner was pushed wide by Alisson.
United's full-backs then teed up big chances for Bruno Fernandes and Marcus Rashford.
Fernandes flashed a header across goal and wide of the right post from Dalot's far-post cross, before Luke Shaw's delivery from the left found Rashford, whose first-time shot was weak.
Casemiro had the ball in the Liverpool net in the 42nd minute but had strayed offside, and the breakthrough came at the other end a minute later.
Andy Robertson played in Gakpo, who cut in from the left and beat a dawdling Raphael Varane before driving a 12-yard strike into the far corner.
Liverpool then made a dream start to the second half as more sloppy United defending resulted in Harvey Elliott crossing from the right, inside the penalty area, for Nunez to nod in from close range.
The third goal was Liverpool at their best. Salah occupied Lisandro Martinez and drew in Shaw, and Gakpo quietly ran into space before being picked out by his teammate, dashing into the 18-yard box and chipping past David de Gea from a tight angle.
It was 4-0 in the 66th minute as Salah smashed in off the underside of the bar after a fortuitous deflection into his path, and 5-0 nine minutes later as Nunez headed in Henderson's cross.
Salah swept in the sixth in the 83rd minute, with United in total disarray, and Firmino, set to leave Liverpool at the end of the season, drilled a seventh.
In the day's other top-flight game, Nottingham Forest and Everton battled out a 2-2 draw, Brennan Johnson scoring twice for Forest to salvage a point after the Merseysiders had twice gone ahead in the first half through Demarai Gray and Abdoulaye Doucoure.
