Sean Sonner scored the opener on seven minutes when he raced on to a Mark Burgess ball over the Dockers back line, with defender Danny Smith making a brave but futile attempt to block the goal-bound shot.
And Woods exploited further hesitancy in the Tilbury defence moments later, Otis Williams stabbing home from close range after Bradley Hewitt headed down Danny Murphy's corner.
That gave the hosts the perfect start to a game in which they were without the suspended John Christian, which allowed Ryan Tackley to make his comeback, although there was no place for new signing Tim O'Mara, a 23-year-old who signed from Spartan South Midlands side Oxhey Jets where he has been top scorer for two seasons and who has 15 to his name this year. Abdul Yoki and Rob Ursell have been released.
At 2-0 down the Dockers responded well, launching a series of forays into the Northwood half and Mitch Swain had to save from Jason Fontaine and twice from Chris Stowe.
Otis Williams was in the thick of the action as Northwood replied, shooting over after Michael Gordon worked the opening before a surging run into the box was snuffed out by the Dockers defence.
The lanky striker also rattled the crossbar just before the break after a sweeping move involving Murphy and Sonner.
Soon after the restart Sonner had an effort disallowed for offside after Danny Power's shot was blocked in a goal-mouth melee and while Tilbury made three changes and continued to threaten through Clinton Hodge in particular, Northwood finally ended any doubt over the outcome midway through the second period.
Gordon delivered the pin-point cross and Murphy, pushed into midfield in Christian's absence, headed home.
Danny Brown replaced the impressive Anthony Page and Joe Cowen made his first appearance since September instead of Otis Williams as Colin Payne took advantage of the 3-0 cushion but his side still had some work to do.
Swain had to deal with shots from Michael Black and Greg Cohen before Gordon went close to adding a fourth goal, attacking from deep in his own half until Jamie Wallace executed a last ditch tackle.
In stoppage time Swain saved well from Fontaine and the Dockers finally got their consolation when Stowe tapped in from close range after the Woods failed to clear Stephane Koffi's overhead kick. NORTHWOOD: Swain, Power, Tackley, Burgess, Hewitt (Orlu), D Williams, Gordon, Page (Brown), Sonner, O Williams (Cowen), Murphy. Subs not used: Figueiredo, Holland. Goals, Woods: Sonner 7; O Williams 10; Murphy 73. Tilbury: Stowe 90+2. Attendance: 98.