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Welling were left to rue their misfortune after being dumped out of the FA Cup by Carlisle on Sunday.
The Wings conceded two penalties and had two arguably better spot-kick appeals turned down themselves.
Plus Carlisle scored a controversial second goal on the stroke of half-time to leave Loui Fazakerley's men with a mountain to climb.
Welling appeared to have weathered the early storm but Kieron St.Aimie - making his first start of the season - gave the ball away cheaply in the 18th minute and Charlie Wyke burst through to put League 2 Carlisle ahead.
George Porter had an excellent claim for a penalty turned down on 29 minutes when he was bundled over by Mark Ellis but referee Simon Hooper turned it down.
Just when it appeared Welling would go into half-time just one goal down, Carlisle claimed a controversial second a minute before the break. Keeper Michael McEntegart appeared to be fouled from the corner and then the ball went in via the arm of Antony Sweeney.
Carlisle were given a generous penalty seven minutes into the second half when Jabo Ibehre went down under challenge from Zach Fagan. But Welling felt justice was done when McEntegart saved Danny Grainger's spot-kick.
Just three minutes later Welling had another penalty appeal turned down when Michael Bakare burst clear and cut back inside, appearing to have his heels clipped. But referee Hooper was again unmoved.
The game was effectively over on 66 minutes when Carlisle got a second penalty and Harry Osborne was sent-off for his challenge on Sweeney, who went down easily in the penalty area. This time Grainger made no mistake from the spot.
A fourth goal arrived five minutes later when McEntegart parried a right-wing cross and Wyke smashed home the loose ball.
Welling nearly got the goal they deserved a minute later but Bakare was unable to convert Barney Williams' excellent right-wing cross.
Welling's day was summed up in the 89th miunute when Sam Corne's free-kick came back off the angle of bar and post.
Within a minute, Welling's misery was complete when Wyke slotted home his hat-trick goal from close range.
Welling: McEntegart, Jefford, Fagan (Lee 57mins), Osborne, Chambers, Porter, St.Aimie (Harris 62mins), Wellard, Corne, Williams, Bakare (Kabba 77mins). Subs not used: Aksoy, Adeyinka, Lokko, Vidal.
Attendance: 2,028.