The visitors had actually started proceedings in confident form, front rower Ceri Jones burrowing over from a lineout drive in the fourth minute and former Irish international Paul Burke landing the conversion to put Harlequins up by 7-0.
But with Saracens hitting their groove, Harlequins were left chasing shadows for much of the rest of the half, Goode inspiring some fine attacking rugby from his talented backline.
With Goode Kicking a drop-goal and two quickfire penalties to put his side in the lead, Saracens conjured up an exceptional try from nowhere, former Rugby League star Nathan McAvoy racing upfield before off-loading a scoring pass to French World Cup discard Thomas Castaignede.
Goode converted the score and the sides went into the second half with Saracens defending a 19-12 lead.
But the home side were swift out of the blocks after the break, Goode on target with two early penalties before Richard Haughton and Taine Randell completed the try-scoring to inflict the first defeat of the season on Harlequins.
A late fightback saved some face for the visitors, but it was too late in the day to salvage the result.
For Saracens:Tries: Castaignede, Haughton, RandellCons: Goode 3Pens: Goode 5 Drop-goal: Goode
For NEC Harlequins:Tries: Jones, Keogh, PenaltyCons: Burke, Dunne 2 Pens: Burke 3, Dunne