They ran in four tries, and Jeremy Staunton's solid boot kept them far away in the lead with five penalties.
To compound Newcastle's misery, Staunton's opposite number Jonny Wilkinson, who had been in good goal-shooting form, was taken off injured after 34 minutes having taken a hefty knock to the knee.
Staunton and Wilkinson shared four penalty kicks between them to leave the scores tied at six apiece early on, but Quins took the initiative at the end of the first quarter with the game's opening try by George Harder, converted by Staunton.
Semo Sititi brought the visitors back into it with a well-worked try on the burst of his own, and Wilkinson drew the Falcons level with his conversion.
Newcastle's forward defence looked suspect all the way through though, and prop Jim Evans scored five minutes before the break to re-establish Quins' lead.
Again Staunton converted, and then added a penalty on the stroke of half-time for a 23-13 advantage from an open and exciting game.
Newcastle opened the second half in barnstorming fashion, and Mark Mayerhofler put Newcastle back within touching distance with a try, which Dave Walder converted in Jonny Wilkinson's absence.
Quins held firm after that, and Tani Fuga restored the lead with a good try from a catch-and-drive at line-out time.
Staunton missed the conversion, but added a penalty on the hour mark to cancel out one by Walder on 52 minutes, leaving the score at 31-23.
Tom Williams sealed both win and bonus point with a well-taken try on the wing following more good work from Harder, and Staunton's penalty with five minutes to go was the final nail in Newcastle's coffin.
The win lifts Quins to eighth in the table, thus easing their relegation worries, and keeps Newcastle sweating over their possible Heineken Cup qualification after wins by rival clubs.
For Quins:Tries: Harder, Evans, Fuga, WilliamsCons: Staunton 2Pens: Staunton 5
For Newcastle:Tries: Sititi, MayerhoflerCons: Wilkinson, WalderPens: Wilkinson 2, Walder
NEC Harlequins: 15 Tom Williams, 14 George Harder, 13 Dafydd James, 12 Mel Deane, 11 Ugo Monye, 10 Jeremy Staunton, 9 Steve So’oialo, 8 Tony Diprose, 7 André Vos (captain), 6 Nick Easter, 5 Simon Miall, 4 Jim Evans, 3 Ceri Jones, 2 Tani Fuga, 1 Mike WorsleyReplacements: 16 Ace Tiatia, 17 Jon Dawson, 18 Roy Winters, 19 Luke Sherriff, 20 Simon Keogh, 21 Arwel Thomas, 22 Dave von Hoesslin
Newcastle Falcons: 15 Dave Walder, 14 Ollie Phillips, 13 Tom May, 12 Mark Mayerhofler, 11 Michael Stephenson, 10 Jonny Wilkinson, 9 James Grindal, 8 Semo Sititi, 7 Cory Harris, 6 Mike McCarthy, 5 Craig Hamilton, 4 Luke Gross, 3 Micky Ward, 2 Andy Long, 1 Ian Peel (captain).Replacements: 16 James Isaacson, 17 Galo Alvarez Quinones, 18 Geoff Parling, 19 Phil Dowson, 20 Mark Wilkinson, 21 Hall Charlton, 22 Toby Flood
Referee: Ashley RowdenTouch judges: Ashley Reay, Brian CampsallAssessor: Gary Welsh.