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Welling fluffed their lines as they missed the chance to reach the first round of the FA Cup for the first time since 2005 on Saturday.
The Wings were totally outplayed by their Blue Square Bet North visitors who fully deserved a home tie with Hastings in the next round.
Despite a bright start which saw Theo Fairweather-Johnson fire over at full stretch inside the first two minutes, Welling struggled to cope with the power of Reneil Sappleton up front or the midfield guile of Steve Cawley and ex-Tottenham youngster Jesse Waller-Lassen.
An early slip by Ben Martin let in Sappleton but keeper Sam Mott beat his shot away, while it was a role reversal just before the half-hour as Mott's punch fell to Phil Anderson, whose drive was diverted behind by Martin.
Keirnan Hughes-Mason's weak finish lacked conviction and the Wings fell behind nine minutes before half-time. Video evidence later suggested that referee Paul Harris' call to penalise Anthony Acheampong's challenge on Sappleton was wrong on both counts - he made contact with the ball outside the box - but it did not affect the bustly striker who fired his spot-kick beyond Mott.
Mott then turned aside Harry Milton's effort, only for Anthony Sinclair-Furlonge to head in the resulting corner at the far post two minutes before half-time.
Welling needed to claim the next goal but Lafayette hurried his shot wide when he had more time and Fraser Franks, pictured, headed over from a Joe Healy corner. The misses proved costly as Welling made a mess of clearing their lines and Franks' handball in the box was penalised with another penalty and a red card midway through the second half.
Sappleton stepped up to score his second of the afternoon and while Lafayette continued to run for every lost cause, it was a fruitless final half-hour for the hosts until substitute Jon Main fired in during the fourth minute of stoppage time.
There was better news for Bromley, however, who are through to the FA Cup first round proper for the third time in four seasons after they scored a late winner to knock out Worcester.
The Lillywhites came under sustained pressure from the Blue Square Bet North side at Hayes Lane.
Their task was made even harder when Moses Swaibu was sent off for a second bookable offence with 15 minutes left.
However, Bromley stunned the visitors when Ali Fuseini collected the ball on the right flank and crossed for Richard Pacquette to slide home a 90th-minute winner.
Mark Goldberg’s side survived a stoppage-time onslaught and they will now travel to League 2 Fleetwood Town on the weekend of November 3.