In truth the scoreline flattered the visitors who, had it not been for the heroics of keeper Rhys Madden, could have been hugely embarrassed.
Wingate & Finchley hit the post twice in the same move in the first half, after Ahmet Rifat had walked through the defence, Tim Lees took over and sent the first effort onto the inside of the left post - and then Kieran Street struck the opposite post from the rebound.
The Blues dominated possession and front pair Chris Chase and Wayne Grant peppered the goal from distance but Madden saved everything expertly.
The second half continued in the same vein as Wingate controlled the play with Lees and Rifat at their creative best on the ball. Lees however fired wildly over from 6 yards, and saw a one-on-one brilliantly saved as Witham continued to hold out.
Chris Chase was denied by a save from 20 yards high to the keeper's left, and then when a goal was disallowed for offside it appeared that it was going to be ‘one of those days' for Wingate. Finally the breakthrough came in the 80th when Kieran Street struck ferociously from 30 yards with a drive into the bottom right corner that no keeper could have saved. When Steve Velandia was tripped in the box the referee pointed to the spot and Grant scored the penalty to seal the win.
As tempers flared late in the game Witham Town were reduced to ten men, but this had little effect on the heavily one sided match, and Wingate & Finchley comfortably put themselves into Monday's second qualifying round draw.
Assistant Manager Ben Winston was pleased with the performance: "I felt we dominated the game but were patient when things weren't going our way. What was most pleasing was we kept out discipline at times when it could have boiled over. Now we will look forward to the next round."
Wingate & Finchley: Gavin King, Marc Weatherstone (Ola Williams 88), Kieran Street, Craig Ellis, Bobby Aisien, Michael Sacks, Ahmet Rifat, Marvin Samuel, Wayne Grant, Chris Chase (Dean WIlliams 73), Tim Lees (Steve Velandia 65). Subs: Callum Horton, Daniel Clarke, Anthony Limbrick, Joe O'Brien