The Wings, looking to make it seven straight appearances in the second round, provided the passion and the drama in the first half as the Rebels failed to click.
But crowd pleaser Owusu provided the inspiration two minutes after the break with Corey Browne adding the matchwinner in the 55th minute to win Slough an away tie against Conference leaders Halifax.
It looked ominous, however, when the Rebels went into half time trailing to Richard Vercesi's 32nd minute strike which was no less the Wings deserved.
Under pressure from their howitzer tactics, Slough's defence creaked, the midfield groaned and a consequent lack of service to the front men left them whistling in the wind.
A shell-shocked Slough had to withstand the bombardment from Mark Watson, Derek Brown and scorer Vercesi designed to exploit keeper Paul Wilkerson's at times suspect handling in the air.
In the end Watson steamed through Slough sweeper Gary McGinnis with a surging run down the right, cut in a drove a low cross which the unmarked Vercesi sidefooted under Wilkerson from point blank range.
It took no time to see how much good manager Brian McDermott's half time roasting did his side - Owusu's moment of magic changed everything instantly.
Pressuring an indecisive Duncan Horton into losing the ball on the edge of the box shortly after the restart, Owusu smartly chipped over Knight to level the scores. Slough snatched the lead eight minutes later when Terry Angus nodded Danny Bolt's inswinging corner to the near post and Browne turned it home with his head from three yards.
The makeover was complete and a switched on Slough had further chances to seal the result.
The best of these fell to top scorer Owusu, who expertly turned his marker in the closing stages to get in a stinging shot which Knight managed to knock off target in the nick of time.
Welling United Line up
Knight, L Watts, Farley, Perkins : Chapman, Horton, Brown, King, Vercesi, Hanlon, Watson. SUBS: Copley, S Watts (82, for King), Abbott (65, for Watson)